Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
958 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×D4×C22⋊C9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722396 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×C3⋊((C22⋊C9)⋊C4) | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C4×C3⋊((C22⋊C9)⋊C2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11722377 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10596277 | — | 3 | 1 | no | maximal |
| 7 | #10593089 | — | 3 | 3 | no | maximal |
| 8 | C22×C3×C22⋊C9 | C22 | 1 | 2 | yes | — |
| 9 | C2×C3⋊((C22⋊C9)⋊C2) | C22 | 1 | 1 | yes | characteristic |
| 10 | #88742 | — | 4 | 1 | no | maximal |
| 11 | C3×C4×C22⋊C9 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3⋊((C22⋊C9)⋊C4) | C22 | 1 | 2 | yes | — |
| 13 | C3⋊((C22⋊C9)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×C32×D4 | D3 | 1 | 1 | yes | characteristic |
| 15 | C2×#3830 | — | 3 | 1 | no | — |
| 16 | #64162 | — | 3 | 2 | no | — |
| 17 | C2×#3757 | — | 3 | 2 | no | — |
| 18 | #64148 | — | 3 | 2 | no | — |
| 19 | #64147 | — | 3 | 1 | no | — |
| 20 | #64145 | — | 3 | 1 | no | — |
| 21 | #64144 | — | 3 | 2 | no | — |
| 22 | D4×C3⋊Dic3 | — | 3 | 1 | no | — |
| 23 | C4×#638 | — | 3 | 1 | no | — |
| 24 | #64133 | — | 3 | 1 | no | — |
| 25 | D4×C22⋊C9 | D3 | 1 | 3 | yes | complemented |
| 26 | #63694 | — | 3 | 6 | no | — |
| 27 | C2×(C22⋊C9)⋊C4 | — | 3 | 6 | no | — |
| 28 | C4×(C22⋊C9)⋊C2 | — | 3 | 3 | no | — |
| 29 | (C22⋊C9)⋊Q8 | — | 3 | 3 | no | — |
| 30 | C2×C3×C22⋊C9 | — | 2 | 2 | no | — |
| 31 | C2×C3×C22⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 32 | C3⋊((C22⋊C9)⋊C2) | — | 2 | 1 | no | — |
| 33 | C3×D4×C9 | — | 4 | 1 | no | — |
| 34 | #6233 | — | 4 | 2 | no | — |
| 35 | C2×C3⋊Dic9 | — | 4 | 2 | no | — |
| 36 | C4×C3⋊D9 | — | 4 | 1 | no | — |
| 37 | #6226 | — | 4 | 1 | no | — |
| 38 | #5806 | — | 9 | 3 | no | — |
| 39 | #5806 | — | 9 | 1 | no | — |
| 40 | C24×C32 | C2×D3 | 1 | 2 | yes | — |
| 41 | C2×C32×D4 | — | 3 | 1 | no | — |
| 42 | C2×C32×D4 | — | 3 | 2 | no | — |
| 43 | C2×C32×D4 | — | 3 | 1 | no | — |
| 44 | C22×C32×C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 45 | C2×#638 | — | 3 | 2 | no | — |
| 46 | C2×#638 | — | 3 | 1 | no | — |
| 47 | C2×#638 | — | 3 | 2 | no | — |
| 48 | C22×C3⋊Dic3 | — | 3 | 2 | no | — |
| 49 | C22×C3⋊Dic3 | — | 3 | 2 | no | — |
| 50 | #3830 | — | 6 | 2 | no | — |
| 51 | #3830 | — | 6 | 1 | no | — |
| 52 | #3830 | — | 6 | 1 | no | — |
| 53 | C2×C4×C3⋊D3 | — | 3 | 1 | no | — |
| 54 | C2×#634 | — | 3 | 1 | no | — |
| 55 | C22×C22⋊C9 | C2×D3 | 1 | 6 | yes | — |
| 56 | C2×(C22⋊C9)⋊C2 | — | 3 | 3 | no | — |
| 57 | #3757 | — | 3 | 2 | no | — |
| 58 | #3757 | — | 3 | 2 | no | — |
| 59 | #3757 | — | 3 | 2 | no | — |
| 60 | #3757 | — | 3 | 2 | no | — |
| 61 | #3757 | — | 3 | 2 | no | — |
| 62 | #3757 | — | 3 | 1 | no | — |
| 63 | #3752 | — | 3 | 1 | no | — |
| 64 | C4⋊(C3⋊Dic3) | — | 3 | 1 | no | — |
| 65 | #3750 | — | 3 | 2 | no | — |
| 66 | #3750 | — | 3 | 1 | no | — |
| 67 | C4×C3⋊Dic3 | — | 3 | 1 | no | — |
| 68 | #3699 | — | 12 | 3 | no | — |
| 69 | C4×C22⋊C9 | C2×D3 | 1 | 3 | yes | — |
| 70 | (C22⋊C9)⋊C4 | — | 3 | 6 | no | — |
| 71 | (C22⋊C9)⋊C4 | — | 3 | 3 | no | — |
| 72 | C22×C3×C9 | — | 4 | 2 | no | — |
| 73 | C2×C3⋊D9 | — | 4 | 1 | no | — |
| 74 | C3×C22⋊C9 | #41 | 1 | 1 | yes | characteristic, complemented |
| 75 | C3×C4×C9 | — | 4 | 1 | no | — |
| 76 | C3⋊Dic9 | — | 4 | 2 | no | — |
| 77 | C3⋊Dic9 | — | 4 | 1 | no | — |
| 78 | C22×C3×D4 | D9 | 1 | 3 | yes | complemented |
| 79 | C22×C3×D4 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 80 | C2×#237 | — | 9 | 3 | no | — |
| 81 | C2×#237 | — | 9 | 1 | no | — |
| 82 | #953 | — | 9 | 6 | no | — |
| 83 | #953 | — | 9 | 2 | no | — |
| 84 | C2×#217 | — | 9 | 6 | no | — |
| 85 | C2×#217 | — | 9 | 2 | no | — |
| 86 | #939 | — | 9 | 6 | no | — |
| 87 | #939 | — | 9 | 2 | no | — |
| 88 | #938 | — | 9 | 3 | no | — |
| 89 | #938 | — | 9 | 1 | no | — |
| 90 | #936 | — | 9 | 3 | no | — |
| 91 | #936 | — | 9 | 1 | no | — |
| 92 | #935 | — | 9 | 6 | no | — |
| 93 | #935 | — | 9 | 2 | no | — |
| 94 | D4×Dic3 | — | 9 | 3 | no | — |
| 95 | D4×Dic3 | — | 9 | 1 | no | — |
| 96 | C4×#67 | — | 9 | 3 | no | — |
| 97 | C4×#67 | — | 9 | 1 | no | — |
| 98 | #924 | — | 9 | 3 | no | — |
| 99 | #924 | — | 9 | 1 | no | — |
| 100 | C23×C32 | — | 2 | 2 | no | — |
| 101 | C23×C32 | — | 3 | 2 | no | — |
| 102 | C23×C32 | — | 3 | 2 | no | — |
| 103 | C23×C32 | — | 6 | 2 | no | — |
| 104 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 105 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 106 | C32×D4 | — | 3 | 2 | no | — |
| 107 | C32×D4 | — | 3 | 1 | no | — |
| 108 | C32×D4 | — | 6 | 1 | no | — |
| 109 | C32×D4 | S4 | 1 | 1 | yes | characteristic |
| 110 | C2×C32×C4 | — | 3 | 1 | no | — |
| 111 | C2×C32×C4 | — | 3 | 1 | no | — |
| 112 | #638 | — | 6 | 2 | no | — |
| 113 | #638 | — | 6 | 1 | no | — |
| 114 | #638 | — | 6 | 1 | no | — |
| 115 | #638 | — | 6 | 2 | no | — |
| 116 | #638 | — | 12 | 2 | no | — |
| 117 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 118 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 119 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 120 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 121 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 122 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 123 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 124 | C2×C3⋊Dic3 | — | 12 | 2 | no | — |
| 125 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 126 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 127 | #634 | — | 6 | 1 | no | — |
| 128 | #634 | — | 6 | 1 | no | — |
| 129 | C2×C22⋊C9 | — | 2 | 6 | no | — |
| 130 | C2×C22⋊C9 | C22×D3 | 1 | 3 | yes | — |
| 131 | (C22⋊C9)⋊C2 | — | 6 | 3 | no | — |
| 132 | D4×C9 | — | 4 | 3 | no | — |
| 133 | #611 | — | 12 | 6 | no | — |
| 134 | C2×Dic9 | — | 12 | 6 | no | — |
| 135 | C4×D9 | — | 12 | 3 | no | — |
| 136 | Dic18 | — | 12 | 3 | no | — |
| 137 | #546 | — | 27 | 1 | no | Sylow |
| 138 | C2×C3×C9 | — | 4 | 1 | no | — |
| 139 | C2×C3×C9 | — | 8 | 2 | no | — |
| 140 | C3⋊D9 | — | 8 | 1 | no | — |
| 141 | C24×C3 | C2×D9 | 1 | 6 | yes | — |
| 142 | C24×C3 | C2×C3⋊D3 | 1 | 2 | yes | — |
| 143 | C2×C3×D4 | — | 3 | 3 | no | — |
| 144 | C2×C3×D4 | — | 3 | 1 | no | — |
| 145 | C2×C3×D4 | — | 3 | 6 | no | — |
| 146 | C2×C3×D4 | — | 3 | 2 | no | — |
| 147 | C2×C3×D4 | — | 3 | 3 | no | — |
| 148 | C2×C3×D4 | — | 3 | 1 | no | — |
| 149 | C22×C3×C4 | C2×D9 | 1 | 3 | yes | — |
| 150 | C22×C3×C4 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 151 | C2×#67 | — | 9 | 2 | no | — |
| 152 | C2×#67 | — | 9 | 6 | no | — |
| 153 | C2×#67 | — | 9 | 3 | no | — |
| 154 | C2×#67 | — | 9 | 1 | no | — |
| 155 | C2×#67 | — | 9 | 6 | no | — |
| 156 | C2×#67 | — | 9 | 2 | no | — |
| 157 | C22×Dic3 | — | 9 | 2 | no | — |
| 158 | C22×Dic3 | — | 9 | 6 | no | — |
| 159 | C22×Dic3 | — | 9 | 2 | no | — |
| 160 | C22×Dic3 | — | 9 | 6 | no | — |
| 161 | #237 | — | 18 | 2 | no | — |
| 162 | #237 | — | 18 | 6 | no | — |
| 163 | #237 | — | 18 | 1 | no | — |
| 164 | #237 | — | 18 | 3 | no | — |
| 165 | #237 | — | 18 | 3 | no | — |
| 166 | #237 | — | 18 | 1 | no | — |
| 167 | C2×C4×D3 | — | 9 | 1 | no | — |
| 168 | C2×C4×D3 | — | 9 | 3 | no | — |
| 169 | C2×Dic6 | — | 9 | 1 | no | — |
| 170 | C2×Dic6 | — | 9 | 3 | no | — |
| 171 | #217 | — | 9 | 2 | no | — |
| 172 | #217 | — | 9 | 6 | no | — |
| 173 | #217 | — | 9 | 6 | no | — |
| 174 | #217 | — | 9 | 2 | no | — |
| 175 | #217 | — | 9 | 6 | no | — |
| 176 | #217 | — | 9 | 2 | no | — |
| 177 | #217 | — | 9 | 6 | no | — |
| 178 | #217 | — | 9 | 2 | no | — |
| 179 | #217 | — | 9 | 6 | no | — |
| 180 | #217 | — | 9 | 3 | no | — |
| 181 | #217 | — | 9 | 2 | no | — |
| 182 | #217 | — | 9 | 1 | no | — |
| 183 | (C2×D3)⋊C4 | — | 9 | 3 | no | — |
| 184 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 185 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 186 | C4⋊Dic3 | — | 9 | 3 | no | — |
| 187 | Dic3⋊C4 | — | 9 | 6 | no | — |
| 188 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 189 | Dic3⋊C4 | — | 9 | 3 | no | — |
| 190 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 191 | C4×Dic3 | — | 9 | 1 | no | — |
| 192 | C4×Dic3 | — | 9 | 3 | no | — |
| 193 | C22×C32 | — | 3 | 1 | no | — |
| 194 | C22×C32 | — | 3 | 1 | no | — |
| 195 | C22×C32 | — | 3 | 2 | no | — |
| 196 | C22×C32 | — | 6 | 2 | no | — |
| 197 | C22×C32 | — | 6 | 2 | no | — |
| 198 | C22×C32 | — | 6 | 2 | no | — |
| 199 | C22×C32 | — | 6 | 2 | no | — |
| 200 | C22×C32 | #237 | 1 | 1 | yes | characteristic |
| 201 | C22×C32 | C2×S4 | 1 | 2 | yes | — |
| 202 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 203 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 204 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 205 | C32×C4 | — | 3 | 1 | no | — |
| 206 | C32×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 207 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 208 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 209 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 210 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 211 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 212 | C22×C9 | — | 4 | 6 | no | — |
| 213 | C2×D9 | — | 12 | 3 | no | — |
| 214 | C22⋊C9 | #237 | 1 | 3 | yes | complemented |
| 215 | C4×C9 | — | 4 | 3 | no | — |
| 216 | Dic9 | — | 12 | 6 | no | — |
| 217 | Dic9 | — | 12 | 3 | no | — |
| 218 | C2×#41 | — | 27 | 1 | no | — |
| 219 | C22×D4 | C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 220 | #124 | — | 27 | 1 | no | — |
| 221 | #123 | — | 27 | 2 | no | — |
| 222 | C22⋊Q8 | — | 27 | 1 | no | — |
| 223 | #121 | — | 27 | 1 | no | — |
| 224 | #121 | — | 27 | 2 | no | — |
| 225 | #120 | — | 27 | 2 | no | — |
| 226 | C4×D4 | — | 27 | 1 | no | — |
| 227 | C4×D4 | — | 27 | 1 | no | — |
| 228 | C2×C22⋊C4 | — | 27 | 2 | no | — |
| 229 | C3×C9 | — | 4 | 1 | no | Sylow |
| 230 | C23×C3 | — | 2 | 6 | no | — |
| 231 | C23×C3 | — | 2 | 2 | no | — |
| 232 | C23×C3 | — | 3 | 6 | no | — |
| 233 | C23×C3 | — | 3 | 2 | no | — |
| 234 | C23×C3 | — | 3 | 2 | no | — |
| 235 | C23×C3 | — | 3 | 6 | no | — |
| 236 | C23×C3 | — | 6 | 6 | no | — |
| 237 | C23×C3 | — | 6 | 2 | no | — |
| 238 | C23×C3 | C22×D9 | 1 | 3 | yes | — |
| 239 | C23×C3 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 240 | C22×D3 | — | 9 | 1 | no | — |
| 241 | C22×D3 | — | 9 | 3 | no | — |
| 242 | C3×D4 | — | 3 | 2 | no | — |
| 243 | C3×D4 | — | 3 | 6 | no | — |
| 244 | C3×D4 | — | 3 | 1 | no | — |
| 245 | C3×D4 | — | 3 | 3 | no | — |
| 246 | C3×D4 | — | 6 | 1 | no | — |
| 247 | C3×D4 | — | 6 | 3 | no | — |
| 248 | C3×D4 | (C22⋊C9)⋊C2 | 1 | 3 | yes | complemented |
| 249 | C3×D4 | C3⋊S4 | 1 | 1 | yes | characteristic |
| 250 | C2×C3×C4 | — | 3 | 1 | no | — |
| 251 | C2×C3×C4 | — | 3 | 3 | no | — |
| 252 | C2×C3×C4 | — | 3 | 3 | no | — |
| 253 | C2×C3×C4 | — | 3 | 1 | no | — |
| 254 | #67 | — | 18 | 2 | no | — |
| 255 | #67 | — | 18 | 6 | no | — |
| 256 | #67 | — | 18 | 3 | no | — |
| 257 | #67 | — | 18 | 1 | no | — |
| 258 | #67 | — | 18 | 2 | no | — |
| 259 | #67 | — | 18 | 3 | no | — |
| 260 | #67 | — | 18 | 6 | no | — |
| 261 | #67 | — | 18 | 1 | no | — |
| 262 | #67 | — | 36 | 6 | no | — |
| 263 | #67 | — | 36 | 2 | no | — |
| 264 | C2×Dic3 | — | 9 | 1 | no | — |
| 265 | C2×Dic3 | — | 9 | 3 | no | — |
| 266 | C2×Dic3 | — | 9 | 1 | no | — |
| 267 | C2×Dic3 | — | 9 | 3 | no | — |
| 268 | C2×Dic3 | — | 9 | 2 | no | — |
| 269 | C2×Dic3 | — | 9 | 6 | no | — |
| 270 | C2×Dic3 | — | 9 | 2 | no | — |
| 271 | C2×Dic3 | — | 9 | 6 | no | — |
| 272 | C2×Dic3 | — | 9 | 1 | no | — |
| 273 | C2×Dic3 | — | 9 | 3 | no | — |
| 274 | C2×Dic3 | — | 18 | 2 | no | — |
| 275 | C2×Dic3 | — | 18 | 6 | no | — |
| 276 | C2×Dic3 | — | 18 | 2 | no | — |
| 277 | C2×Dic3 | — | 18 | 6 | no | — |
| 278 | C2×Dic3 | — | 36 | 6 | no | — |
| 279 | C2×Dic3 | — | 36 | 2 | no | — |
| 280 | C4×D3 | — | 18 | 1 | no | — |
| 281 | C4×D3 | — | 18 | 3 | no | — |
| 282 | C4×D3 | — | 18 | 1 | no | — |
| 283 | C4×D3 | — | 18 | 3 | no | — |
| 284 | Dic6 | — | 18 | 1 | no | — |
| 285 | Dic6 | — | 18 | 3 | no | — |
| 286 | Dic6 | — | 18 | 1 | no | — |
| 287 | Dic6 | — | 18 | 3 | no | — |
| 288 | C2×C32 | — | 2 | 2 | no | — |
| 289 | C2×C32 | — | 3 | 1 | no | — |
| 290 | C2×C32 | — | 3 | 1 | no | — |
| 291 | C2×C32 | — | 6 | 2 | no | — |
| 292 | C2×C32 | C22×S4 | 1 | 1 | yes | characteristic |
| 293 | C3⋊D3 | — | 12 | 1 | no | — |
| 294 | C2×C9 | — | 4 | 3 | no | — |
| 295 | C2×C9 | — | 8 | 6 | no | — |
| 296 | D9 | — | 24 | 3 | no | — |
| 297 | C24 | C2×C3⋊D9 | 1 | 2 | yes | — |
| 298 | #41 | — | 54 | 2 | no | — |
| 299 | #41 | — | 54 | 1 | no | — |
| 300 | #41 | — | 54 | 1 | no | — |
| 301 | C2×Q8 | — | 27 | 1 | no | — |
| 302 | C2×D4 | — | 3 | 1 | no | — |
| 303 | C2×D4 | — | 3 | 2 | no | — |
| 304 | C2×D4 | — | 3 | 1 | no | — |
| 305 | C2×D4 | — | 27 | 2 | no | — |
| 306 | C2×D4 | — | 27 | 1 | no | — |
| 307 | C2×D4 | — | 27 | 2 | no | — |
| 308 | C22×C4 | — | 27 | 1 | no | — |
| 309 | C22×C4 | — | 27 | 2 | no | — |
| 310 | C22×C4 | — | 27 | 2 | no | — |
| 311 | C22×C4 | C2×C3⋊D9 | 1 | 1 | yes | characteristic |
| 312 | C4⋊C4 | — | 27 | 1 | no | — |
| 313 | C4⋊C4 | — | 27 | 1 | no | — |
| 314 | C4⋊C4 | — | 27 | 2 | no | — |
| 315 | C22⋊C4 | — | 27 | 1 | no | — |
| 316 | C22⋊C4 | — | 27 | 2 | no | — |
| 317 | C22⋊C4 | — | 27 | 2 | no | — |
| 318 | C22⋊C4 | — | 27 | 2 | no | — |
| 319 | C22⋊C4 | — | 27 | 2 | no | — |
| 320 | C22⋊C4 | — | 27 | 1 | no | — |
| 321 | C22⋊C4 | — | 27 | 2 | no | — |
| 322 | C42 | — | 27 | 1 | no | — |
| 323 | C22×C3 | — | 3 | 3 | no | — |
| 324 | C22×C3 | — | 3 | 1 | no | — |
| 325 | C22×C3 | — | 3 | 1 | no | — |
| 326 | C22×C3 | — | 3 | 3 | no | — |
| 327 | C22×C3 | — | 3 | 2 | no | — |
| 328 | C22×C3 | — | 3 | 6 | no | — |
| 329 | C22×C3 | — | 6 | 6 | no | — |
| 330 | C22×C3 | — | 6 | 2 | no | — |
| 331 | C22×C3 | — | 6 | 6 | no | — |
| 332 | C22×C3 | — | 6 | 2 | no | — |
| 333 | C22×C3 | — | 6 | 6 | no | — |
| 334 | C22×C3 | — | 6 | 2 | no | — |
| 335 | C22×C3 | — | 6 | 6 | no | — |
| 336 | C22×C3 | — | 6 | 2 | no | — |
| 337 | C22×C3 | #3699 | 1 | 3 | yes | complemented |
| 338 | C22×C3 | C2×(C22⋊C9)⋊C2 | 1 | 6 | yes | — |
| 339 | C22×C3 | #3830 | 1 | 1 | yes | characteristic |
| 340 | C22×C3 | C2×C3⋊S4 | 1 | 2 | yes | — |
| 341 | C2×D3 | — | 18 | 3 | no | — |
| 342 | C2×D3 | — | 18 | 1 | no | — |
| 343 | C2×D3 | — | 18 | 3 | no | — |
| 344 | C2×D3 | — | 18 | 1 | no | — |
| 345 | C2×D3 | — | 18 | 1 | no | — |
| 346 | C2×D3 | — | 18 | 3 | no | — |
| 347 | C3×C4 | — | 3 | 1 | no | — |
| 348 | C3×C4 | — | 3 | 3 | no | — |
| 349 | C3×C4 | C2×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 350 | C3×C4 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 351 | Dic3 | — | 18 | 3 | no | — |
| 352 | Dic3 | — | 18 | 1 | no | — |
| 353 | Dic3 | — | 18 | 6 | no | — |
| 354 | Dic3 | — | 18 | 2 | no | — |
| 355 | Dic3 | — | 18 | 3 | no | — |
| 356 | Dic3 | — | 18 | 1 | no | — |
| 357 | Dic3 | — | 18 | 2 | no | — |
| 358 | Dic3 | — | 18 | 1 | no | — |
| 359 | Dic3 | — | 18 | 6 | no | — |
| 360 | Dic3 | — | 18 | 3 | no | — |
| 361 | C32 | #5914 | 1 | 1 | yes | characteristic |
| 362 | C9 | — | 4 | 3 | no | — |
| 363 | C23 | — | 2 | 2 | no | — |
| 364 | C23 | — | 3 | 2 | no | — |
| 365 | C23 | — | 3 | 2 | no | — |
| 366 | C23 | — | 6 | 2 | no | — |
| 367 | C23 | — | 27 | 1 | no | — |
| 368 | C23 | C22×C3⋊D9 | 1 | 1 | yes | characteristic |
| 369 | Q8 | — | 54 | 1 | no | — |
| 370 | Q8 | — | 54 | 1 | no | — |
| 371 | D4 | — | 3 | 2 | no | — |
| 372 | D4 | — | 3 | 1 | no | — |
| 373 | D4 | — | 6 | 1 | no | — |
| 374 | D4 | — | 54 | 2 | no | — |
| 375 | D4 | — | 54 | 1 | no | — |
| 376 | D4 | — | 54 | 2 | no | — |
| 377 | D4 | — | 54 | 1 | no | — |
| 378 | D4 | — | 108 | 2 | no | — |
| 379 | D4 | C3⋊((C22⋊C9)⋊C2) | 1 | 1 | yes | characteristic, complemented |
| 380 | C2×C4 | — | 3 | 1 | no | — |
| 381 | C2×C4 | — | 3 | 1 | no | — |
| 382 | C2×C4 | — | 27 | 1 | no | — |
| 383 | C2×C4 | — | 27 | 1 | no | — |
| 384 | C2×C4 | — | 27 | 2 | no | — |
| 385 | C2×C4 | — | 27 | 1 | no | — |
| 386 | C2×C4 | — | 27 | 2 | no | — |
| 387 | C2×C4 | — | 54 | 1 | no | — |
| 388 | C2×C4 | — | 54 | 2 | no | — |
| 389 | C2×C4 | — | 54 | 2 | no | — |
| 390 | C2×C4 | — | 54 | 1 | no | — |
| 391 | C2×C4 | — | 108 | 2 | no | — |
| 392 | C2×C3 | — | 2 | 6 | no | — |
| 393 | C2×C3 | — | 2 | 2 | no | — |
| 394 | C2×C3 | — | 3 | 3 | no | — |
| 395 | C2×C3 | — | 3 | 3 | no | — |
| 396 | C2×C3 | — | 3 | 1 | no | — |
| 397 | C2×C3 | — | 3 | 1 | no | — |
| 398 | C2×C3 | — | 6 | 6 | no | — |
| 399 | C2×C3 | — | 6 | 2 | no | — |
| 400 | C2×C3 | C22×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 401 | C2×C3 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 402 | D3 | — | 36 | 3 | no | — |
| 403 | D3 | — | 36 | 1 | no | — |
| 404 | C22 | — | 3 | 1 | no | — |
| 405 | C22 | — | 3 | 1 | no | — |
| 406 | C22 | — | 3 | 2 | no | — |
| 407 | C22 | — | 6 | 2 | no | — |
| 408 | C22 | — | 6 | 2 | no | — |
| 409 | C22 | — | 6 | 2 | no | — |
| 410 | C22 | — | 6 | 2 | no | — |
| 411 | C22 | — | 54 | 1 | no | — |
| 412 | C22 | — | 54 | 1 | no | — |
| 413 | C22 | — | 54 | 1 | no | — |
| 414 | C22 | #88742 | 1 | 1 | yes | characteristic, complemented |
| 415 | C22 | C2×C3⋊((C22⋊C9)⋊C2) | 1 | 2 | yes | — |
| 416 | C4 | — | 3 | 1 | no | — |
| 417 | C4 | — | 54 | 1 | no | — |
| 418 | C4 | — | 54 | 2 | no | — |
| 419 | C4 | — | 54 | 1 | no | — |
| 420 | C4 | — | 54 | 1 | no | — |
| 421 | C4 | — | 54 | 2 | no | — |
| 422 | C4 | C2×C3⋊((C22⋊C9)⋊C2) | 1 | 1 | yes | characteristic |
| 423 | C3 | #10593089 | 1 | 3 | yes | complemented |
| 424 | C3 | #10596577 | 1 | 1 | yes | characteristic |
| 425 | C2 | — | 2 | 2 | no | — |
| 426 | C2 | — | 3 | 1 | no | — |
| 427 | C2 | — | 3 | 1 | no | — |
| 428 | C2 | — | 6 | 2 | no | — |
| 429 | C2 | — | 108 | 1 | no | — |
| 430 | C2 | C22×C3⋊((C22⋊C9)⋊C2) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×D4×C22⋊C9 | C2 | semidirect |
| 2. #11722396 | C2 | semidirect |
| 3. C2×C3⋊((C22⋊C9)⋊C4) | C2 | semidirect |
| 4. C4×C3⋊((C22⋊C9)⋊C2) | C2 | semidirect |
| 5. #11722377 | C2 | semidirect |
| 25. D4×C22⋊C9 | D3 | semidirect |
| 74. C3×C22⋊C9 | #41 | semidirect |
| 78. C22×C3×D4 | D9 | semidirect |
| 214. C22⋊C9 | #237 | semidirect |
| 219. C22×D4 | C3⋊D9 | semidirect |
| 248. C3×D4 | (C22⋊C9)⋊C2 | semidirect |
| 337. C22×C3 | #3699 | semidirect |
| 379. D4 | C3⋊((C22⋊C9)⋊C2) | semidirect |
| 414. C22 | #88742 | semidirect |
| 423. C3 | #10593089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×C22⋊C9 | 2 |
| #11722396 | 2 |
| C2×C3⋊((C22⋊C9)⋊C4) | 2 |
| C4×C3⋊((C22⋊C9)⋊C2) | 2 |
| #11722377 | 2 |
| #10596277 | 3 |
| #10593089 | 3 |
| #88742 | 4 |