Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
432 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 51 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 | Q8×C3⋊#157 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724315 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11723708 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#63940 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11722763 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722758 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11722757 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10593476 | — | 3 | 1 | no | maximal |
| 9 | C2×D32⋊D3 | — | 2 | 1 | no | — |
| 10 | C2×D32⋊D3 | — | 2 | 1 | no | — |
| 11 | C3×Q8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 12 | C4⋊#1113 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×#3802 | C22 | 1 | 1 | yes | characteristic |
| 14 | C4⋊(C3⋊#157) | — | 2 | 1 | no | — |
| 15 | C4⋊(C3⋊#157) | C22 | 1 | 1 | yes | characteristic |
| 16 | C4×C3⋊#157 | — | 2 | 1 | no | — |
| 17 | C4×C3⋊#157 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#3755 | — | 2 | 1 | no | — |
| 19 | C32×#215 | — | 2 | 1 | no | — |
| 20 | #88811 | — | 2 | 1 | no | — |
| 21 | #88808 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#3716 | — | 2 | 1 | no | — |
| 23 | C3×#3710 | C22 | 1 | 1 | yes | characteristic |
| 24 | Q8×#157 | — | 3 | 1 | no | — |
| 25 | #64231 | — | 3 | 1 | no | — |
| 26 | C3×D3×SD16 | — | 6 | 1 | no | — |
| 27 | #63940 | — | 3 | 1 | no | — |
| 28 | #63940 | D3 | 1 | 1 | yes | characteristic, complemented |
| 29 | D3×#215 | — | 6 | 1 | no | — |
| 30 | #63732 | — | 3 | 1 | no | — |
| 31 | #63729 | — | 3 | 1 | no | — |
| 32 | #63729 | — | 3 | 1 | no | — |
| 33 | C2×#1113 | — | 2 | 1 | no | — |
| 34 | C2×C3×D32 | — | 2 | 1 | no | — |
| 35 | C2×C3⋊#157 | — | 2 | 1 | no | — |
| 36 | C2×C3⋊#157 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×C3⋊#157 | D4 | 1 | 1 | yes | characteristic |
| 38 | D32⋊D3 | — | 4 | 2 | no | — |
| 39 | D32⋊D3 | — | 4 | 2 | no | — |
| 40 | C33×Q8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 42 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 43 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 44 | C3×#634 | — | 2 | 1 | no | — |
| 45 | C3×#634 | D4 | 1 | 1 | yes | characteristic, complemented |
| 46 | C32×D12 | — | 2 | 1 | no | — |
| 47 | #6295 | — | 2 | 1 | no | — |
| 48 | C3×#625 | — | 2 | 1 | no | — |
| 49 | C3×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 50 | C32×C3⋊C8 | — | 2 | 1 | no | — |
| 51 | #5163 | — | 9 | 1 | no | maximal |
| 52 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 53 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 54 | Q8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 55 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 56 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 57 | C3×D3×D4 | — | 6 | 1 | no | — |
| 58 | #3802 | — | 3 | 1 | no | — |
| 59 | #3802 | C2×D3 | 1 | 1 | yes | characteristic |
| 60 | D3×D12 | — | 6 | 1 | no | — |
| 61 | C4⋊#157 | — | 3 | 1 | no | — |
| 62 | C4⋊#157 | — | 6 | 1 | no | — |
| 63 | C4×#157 | — | 3 | 1 | no | — |
| 64 | C4×#157 | — | 6 | 1 | no | — |
| 65 | C32×SD16 | — | 6 | 1 | no | — |
| 66 | #3755 | — | 2 | 1 | no | — |
| 67 | C3×#215 | — | 2 | 1 | no | — |
| 68 | C3×#215 | — | 2 | 1 | no | — |
| 69 | C3×#215 | — | 4 | 1 | no | — |
| 70 | C3×#215 | — | 6 | 1 | no | — |
| 71 | C3×#215 | — | 6 | 1 | no | — |
| 72 | C3×#215 | — | 12 | 1 | no | — |
| 73 | C3×#214 | — | 6 | 1 | no | — |
| 74 | C3×#204 | — | 6 | 1 | no | — |
| 75 | C3×D3×C8 | — | 6 | 1 | no | — |
| 76 | #3717 | — | 6 | 1 | no | — |
| 77 | #3716 | — | 2 | 1 | no | — |
| 78 | #3716 | — | 6 | 1 | no | — |
| 79 | #3715 | — | 6 | 1 | no | — |
| 80 | #3710 | — | 3 | 1 | no | — |
| 81 | #3710 | C2×D3 | 1 | 1 | yes | characteristic |
| 82 | D3×C3⋊C8 | — | 6 | 1 | no | — |
| 83 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 84 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C2×C32×D3 | — | 4 | 1 | no | — |
| 86 | #1113 | — | 4 | 1 | no | — |
| 87 | #1113 | — | 4 | 1 | no | — |
| 88 | C3×D32 | — | 4 | 1 | no | — |
| 89 | C3×D32 | — | 4 | 1 | no | — |
| 90 | C3⋊#157 | — | 2 | 1 | no | — |
| 91 | C3⋊#157 | — | 4 | 1 | no | — |
| 92 | C3⋊#157 | SD16 | 1 | 2 | yes | complemented |
| 93 | C33×C4 | — | 2 | 1 | no | — |
| 94 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 96 | C3×C3⋊Dic3 | #41 | 1 | 1 | yes | characteristic |
| 97 | C2×C3×SD16 | — | 9 | 1 | no | — |
| 98 | Q8×Dic3 | — | 9 | 1 | no | — |
| 99 | C2×#215 | — | 9 | 1 | no | — |
| 100 | #940 | — | 9 | 1 | no | — |
| 101 | D3×SD16 | — | 6 | 1 | no | — |
| 102 | D3×SD16 | — | 18 | 1 | no | — |
| 103 | #832 | — | 9 | 1 | no | — |
| 104 | #821 | — | 9 | 1 | no | — |
| 105 | Dic3⋊C8 | — | 9 | 1 | no | — |
| 106 | C22×C3×D3 | — | 12 | 1 | no | — |
| 107 | C2×D32 | — | 2 | 1 | no | — |
| 108 | C2×D32 | — | 6 | 1 | no | — |
| 109 | C2×D32 | — | 12 | 1 | no | — |
| 110 | C2×#157 | — | 3 | 1 | no | — |
| 111 | C2×#157 | — | 3 | 1 | no | — |
| 112 | C2×#157 | — | 6 | 1 | no | — |
| 113 | GO+(4,𝔽2) | — | 12 | 2 | no | — |
| 114 | GO+(4,𝔽2) | — | 12 | 2 | no | — |
| 115 | C32×Q8 | — | 2 | 1 | no | — |
| 116 | C32×Q8 | — | 2 | 1 | no | — |
| 117 | C32×Q8 | — | 4 | 1 | no | — |
| 118 | C32×Q8 | — | 4 | 1 | no | — |
| 119 | C32×Q8 | #67 | 1 | 1 | yes | characteristic, complemented |
| 120 | C32×D4 | — | 6 | 1 | no | — |
| 121 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 122 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 123 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 124 | #634 | — | 2 | 1 | no | — |
| 125 | #634 | #67 | 1 | 1 | yes | characteristic, complemented |
| 126 | C3×#67 | — | 12 | 1 | no | — |
| 127 | C3×D12 | — | 2 | 1 | no | — |
| 128 | C3×D12 | — | 2 | 1 | no | — |
| 129 | C3×D12 | — | 4 | 1 | no | — |
| 130 | C3×D12 | — | 6 | 1 | no | — |
| 131 | C3×D12 | — | 6 | 1 | no | — |
| 132 | C3×D12 | — | 12 | 1 | no | — |
| 133 | C3×C4×D3 | — | 6 | 1 | no | — |
| 134 | C3×C4×D3 | — | 6 | 1 | no | — |
| 135 | C3×C4×D3 | — | 12 | 1 | no | — |
| 136 | C3×C4×D3 | — | 12 | 1 | no | — |
| 137 | C3×Dic6 | — | 6 | 1 | no | — |
| 138 | C3×Dic6 | — | 6 | 1 | no | — |
| 139 | C3×Dic6 | — | 12 | 1 | no | — |
| 140 | C3×Dic6 | — | 12 | 1 | no | — |
| 141 | #626 | — | 12 | 1 | no | — |
| 142 | #625 | — | 2 | 1 | no | — |
| 143 | #625 | — | 6 | 1 | no | — |
| 144 | C32×C8 | — | 6 | 1 | no | — |
| 145 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 146 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 147 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 148 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 149 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 150 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 151 | C3×C3⋊C8 | — | 12 | 1 | no | — |
| 152 | #460 | — | 27 | 1 | no | Sylow |
| 153 | C2×C33 | #121 | 1 | 1 | yes | characteristic |
| 154 | C3×C3⋊D3 | — | 8 | 1 | no | — |
| 155 | C3×C3⋊D3 | C2×SD16 | 1 | 1 | yes | characteristic |
| 156 | C3×C3⋊D3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 157 | C32×D3 | — | 8 | 1 | no | — |
| 158 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 159 | C2×C3×D4 | — | 9 | 1 | no | — |
| 160 | C2×#67 | — | 18 | 1 | no | — |
| 161 | C2×#67 | — | 18 | 1 | no | — |
| 162 | D3×Q8 | — | 6 | 1 | no | — |
| 163 | D3×Q8 | — | 6 | 1 | no | — |
| 164 | D3×D4 | — | 6 | 1 | no | — |
| 165 | D3×D4 | — | 18 | 1 | no | — |
| 166 | C2×D12 | — | 9 | 1 | no | — |
| 167 | C3×SD16 | — | 6 | 1 | no | — |
| 168 | C3×SD16 | — | 6 | 1 | no | — |
| 169 | C3×SD16 | — | 12 | 1 | no | — |
| 170 | C3×SD16 | — | 18 | 1 | no | — |
| 171 | C3×SD16 | — | 18 | 1 | no | — |
| 172 | C2×C3×C8 | — | 9 | 1 | no | — |
| 173 | #215 | — | 2 | 1 | no | — |
| 174 | #215 | — | 6 | 1 | no | — |
| 175 | #215 | — | 6 | 1 | no | — |
| 176 | #215 | — | 12 | 1 | no | — |
| 177 | #215 | — | 18 | 1 | no | — |
| 178 | #214 | — | 6 | 1 | no | — |
| 179 | #214 | — | 18 | 1 | no | — |
| 180 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 181 | C4⋊Dic3 | — | 18 | 1 | no | — |
| 182 | C4×Dic3 | — | 9 | 1 | no | — |
| 183 | C4×Dic3 | — | 18 | 1 | no | — |
| 184 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 185 | #204 | — | 6 | 1 | no | — |
| 186 | #204 | — | 18 | 1 | no | — |
| 187 | D3×C8 | — | 6 | 1 | no | — |
| 188 | D3×C8 | — | 18 | 1 | no | — |
| 189 | C22×C32 | — | 12 | 1 | no | — |
| 190 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 191 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×C3×D3 | — | 4 | 1 | no | — |
| 193 | C2×C3×D3 | — | 4 | 1 | no | — |
| 194 | C2×C3×D3 | — | 6 | 1 | no | — |
| 195 | C2×C3×D3 | — | 6 | 1 | no | — |
| 196 | C2×C3×D3 | — | 8 | 1 | no | — |
| 197 | C2×C3×D3 | — | 12 | 1 | no | — |
| 198 | C2×C3×D3 | — | 12 | 1 | no | — |
| 199 | C2×C3×D3 | — | 24 | 1 | no | — |
| 200 | C2×C3×D3 | — | 24 | 1 | no | — |
| 201 | C2×C3×D3 | — | 24 | 1 | no | — |
| 202 | D32 | — | 4 | 1 | no | — |
| 203 | D32 | — | 4 | 1 | no | — |
| 204 | D32 | — | 12 | 1 | no | — |
| 205 | D32 | — | 12 | 1 | no | — |
| 206 | D32 | — | 24 | 1 | no | — |
| 207 | D32 | — | 24 | 1 | no | — |
| 208 | #157 | — | 3 | 2 | no | — |
| 209 | #157 | — | 6 | 1 | no | — |
| 210 | #157 | — | 12 | 1 | no | — |
| 211 | C32×C4 | — | 2 | 1 | no | — |
| 212 | C32×C4 | — | 2 | 1 | no | — |
| 213 | C32×C4 | — | 2 | 1 | no | — |
| 214 | C32×C4 | — | 4 | 1 | no | — |
| 215 | C32×C4 | — | 4 | 1 | no | — |
| 216 | C32×C4 | — | 4 | 1 | no | — |
| 217 | C32×C4 | — | 4 | 1 | no | — |
| 218 | C32×C4 | — | 8 | 1 | no | — |
| 219 | C32×C4 | — | 8 | 1 | no | — |
| 220 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 221 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 222 | C3⋊Dic3 | #237 | 1 | 1 | yes | characteristic |
| 223 | C3×Dic3 | — | 6 | 1 | no | — |
| 224 | C3×Dic3 | — | 6 | 1 | no | — |
| 225 | C3×Dic3 | — | 12 | 1 | no | — |
| 226 | C3×Dic3 | — | 12 | 1 | no | — |
| 227 | C2×SD16 | — | 9 | 1 | no | — |
| 228 | C2×SD16 | — | 27 | 1 | no | — |
| 229 | #127 | — | 27 | 1 | no | — |
| 230 | C4×Q8 | — | 27 | 1 | no | — |
| 231 | C4⋊C8 | — | 27 | 1 | no | — |
| 232 | #102 | — | 27 | 1 | no | — |
| 233 | #102 | — | 27 | 1 | no | — |
| 234 | C33 | #460 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 235 | C23×C3 | — | 18 | 1 | no | — |
| 236 | C22×D3 | — | 12 | 1 | no | — |
| 237 | C22×D3 | — | 18 | 1 | no | — |
| 238 | C22×D3 | — | 36 | 1 | no | — |
| 239 | C3×Q8 | — | 2 | 1 | no | — |
| 240 | C3×Q8 | — | 2 | 1 | no | — |
| 241 | C3×Q8 | — | 4 | 1 | no | — |
| 242 | C3×Q8 | — | 4 | 1 | no | — |
| 243 | C3×Q8 | — | 9 | 1 | no | — |
| 244 | C3×Q8 | — | 18 | 1 | no | — |
| 245 | C3×Q8 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 246 | C3×D4 | — | 6 | 1 | no | — |
| 247 | C3×D4 | — | 6 | 1 | no | — |
| 248 | C3×D4 | — | 12 | 1 | no | — |
| 249 | C3×D4 | — | 18 | 1 | no | — |
| 250 | C3×D4 | — | 18 | 1 | no | — |
| 251 | C2×C3×C4 | — | 9 | 1 | no | — |
| 252 | C2×C3×C4 | — | 18 | 1 | no | — |
| 253 | #67 | — | 12 | 1 | no | — |
| 254 | #67 | — | 36 | 1 | no | — |
| 255 | #67 | — | 36 | 2 | no | — |
| 256 | #67 | — | 36 | 2 | no | — |
| 257 | C2×Dic3 | — | 9 | 1 | no | — |
| 258 | C2×Dic3 | — | 9 | 1 | no | — |
| 259 | C2×Dic3 | — | 18 | 1 | no | — |
| 260 | D12 | — | 2 | 1 | no | — |
| 261 | D12 | — | 6 | 1 | no | — |
| 262 | D12 | — | 6 | 1 | no | — |
| 263 | D12 | — | 12 | 1 | no | — |
| 264 | D12 | — | 18 | 1 | no | — |
| 265 | C4×D3 | — | 6 | 1 | no | — |
| 266 | C4×D3 | — | 6 | 1 | no | — |
| 267 | C4×D3 | — | 12 | 1 | no | — |
| 268 | C4×D3 | — | 12 | 1 | no | — |
| 269 | Dic6 | — | 6 | 1 | no | — |
| 270 | Dic6 | — | 6 | 1 | no | — |
| 271 | Dic6 | — | 12 | 1 | no | — |
| 272 | Dic6 | — | 12 | 1 | no | — |
| 273 | C3×C8 | — | 6 | 1 | no | — |
| 274 | C3×C8 | — | 6 | 1 | no | — |
| 275 | C3×C8 | — | 12 | 1 | no | — |
| 276 | C3×C8 | — | 18 | 1 | no | — |
| 277 | C3⋊C8 | — | 2 | 1 | no | — |
| 278 | C3⋊C8 | — | 6 | 1 | no | — |
| 279 | C3⋊C8 | — | 6 | 1 | no | — |
| 280 | C3⋊C8 | — | 12 | 1 | no | — |
| 281 | C2×C32 | — | 2 | 1 | no | — |
| 282 | C2×C32 | — | 2 | 1 | no | — |
| 283 | C2×C32 | — | 4 | 1 | no | — |
| 284 | C2×C32 | — | 4 | 1 | no | — |
| 285 | C2×C32 | — | 24 | 1 | no | — |
| 286 | C2×C32 | #939 | 1 | 1 | yes | characteristic |
| 287 | C3⋊D3 | — | 8 | 1 | no | — |
| 288 | C3⋊D3 | D3×SD16 | 1 | 1 | yes | characteristic |
| 289 | C3⋊D3 | #914 | 1 | 1 | yes | characteristic |
| 290 | C3×D3 | — | 6 | 1 | no | — |
| 291 | C3×D3 | — | 6 | 1 | no | — |
| 292 | C3×D3 | — | 6 | 1 | no | — |
| 293 | C3×D3 | — | 6 | 1 | no | — |
| 294 | C3×D3 | — | 8 | 1 | no | — |
| 295 | C3×D3 | — | 8 | 1 | no | — |
| 296 | C3×D3 | — | 16 | 1 | no | — |
| 297 | C3×D3 | — | 24 | 1 | no | — |
| 298 | C3×D3 | — | 24 | 1 | no | — |
| 299 | C3×D3 | — | 48 | 1 | no | — |
| 300 | C2×Q8 | — | 9 | 1 | no | — |
| 301 | C2×D4 | — | 9 | 1 | no | — |
| 302 | C2×D4 | — | 27 | 1 | no | — |
| 303 | C2×D4 | — | 54 | 1 | no | — |
| 304 | C2×D4 | — | 54 | 1 | no | — |
| 305 | SD16 | — | 6 | 1 | no | — |
| 306 | SD16 | — | 18 | 1 | no | — |
| 307 | SD16 | — | 18 | 1 | no | — |
| 308 | SD16 | — | 54 | 1 | no | — |
| 309 | C2×C8 | — | 9 | 1 | no | — |
| 310 | C2×C8 | — | 27 | 1 | no | — |
| 311 | C4⋊C4 | — | 27 | 1 | no | — |
| 312 | C4⋊C4 | — | 54 | 1 | no | — |
| 313 | C42 | — | 27 | 1 | no | — |
| 314 | C42 | — | 54 | 1 | no | — |
| 315 | C22×C3 | — | 9 | 1 | no | — |
| 316 | C22×C3 | — | 12 | 1 | no | — |
| 317 | C22×C3 | — | 12 | 1 | no | — |
| 318 | C22×C3 | — | 24 | 1 | no | — |
| 319 | C22×C3 | — | 36 | 1 | no | — |
| 320 | C22×C3 | — | 36 | 1 | no | — |
| 321 | C22×C3 | — | 36 | 1 | no | — |
| 322 | C2×D3 | — | 4 | 1 | no | — |
| 323 | C2×D3 | — | 6 | 1 | no | — |
| 324 | C2×D3 | — | 6 | 1 | no | — |
| 325 | C2×D3 | — | 12 | 1 | no | — |
| 326 | C2×D3 | — | 12 | 1 | no | — |
| 327 | C2×D3 | — | 24 | 1 | no | — |
| 328 | C2×D3 | — | 24 | 1 | no | — |
| 329 | C2×D3 | — | 24 | 1 | no | — |
| 330 | C2×D3 | — | 36 | 1 | no | — |
| 331 | C2×D3 | — | 36 | 1 | no | — |
| 332 | C2×D3 | — | 72 | 1 | no | — |
| 333 | C2×D3 | — | 72 | 1 | no | — |
| 334 | C3×C4 | — | 2 | 1 | no | — |
| 335 | C3×C4 | — | 2 | 1 | no | — |
| 336 | C3×C4 | — | 2 | 1 | no | — |
| 337 | C3×C4 | — | 4 | 1 | no | — |
| 338 | C3×C4 | — | 4 | 1 | no | — |
| 339 | C3×C4 | — | 4 | 1 | no | — |
| 340 | C3×C4 | — | 4 | 1 | no | — |
| 341 | C3×C4 | — | 8 | 1 | no | — |
| 342 | C3×C4 | — | 8 | 1 | no | — |
| 343 | C3×C4 | — | 9 | 1 | no | — |
| 344 | C3×C4 | — | 18 | 1 | no | — |
| 345 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 346 | Dic3 | — | 6 | 1 | no | — |
| 347 | Dic3 | — | 6 | 1 | no | — |
| 348 | Dic3 | — | 9 | 2 | no | — |
| 349 | Dic3 | — | 12 | 1 | no | — |
| 350 | Dic3 | — | 12 | 1 | no | — |
| 351 | Dic3 | — | 18 | 1 | no | — |
| 352 | Dic3 | — | 36 | 1 | no | — |
| 353 | C32 | — | 2 | 1 | no | — |
| 354 | C32 | — | 2 | 1 | no | — |
| 355 | C32 | — | 4 | 1 | no | — |
| 356 | C32 | — | 4 | 1 | no | — |
| 357 | C32 | #5163 | 1 | 1 | yes | characteristic, complemented |
| 358 | C23 | — | 18 | 1 | no | — |
| 359 | C23 | — | 54 | 1 | no | — |
| 360 | Q8 | — | 9 | 1 | no | — |
| 361 | Q8 | — | 18 | 1 | no | — |
| 362 | Q8 | D32⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 363 | D4 | — | 6 | 1 | no | — |
| 364 | D4 | — | 18 | 1 | no | — |
| 365 | D4 | — | 18 | 1 | no | — |
| 366 | D4 | — | 54 | 1 | no | — |
| 367 | D4 | — | 108 | 2 | no | — |
| 368 | D4 | — | 108 | 2 | no | — |
| 369 | C2×C4 | — | 9 | 1 | no | — |
| 370 | C2×C4 | — | 18 | 1 | no | — |
| 371 | C2×C4 | — | 27 | 1 | no | — |
| 372 | C2×C4 | — | 27 | 1 | no | — |
| 373 | C2×C4 | — | 54 | 1 | no | — |
| 374 | C8 | — | 6 | 1 | no | — |
| 375 | C8 | — | 18 | 1 | no | — |
| 376 | C2×C3 | — | 2 | 1 | no | — |
| 377 | C2×C3 | — | 2 | 1 | no | — |
| 378 | C2×C3 | — | 4 | 1 | no | — |
| 379 | C2×C3 | — | 4 | 1 | no | — |
| 380 | C2×C3 | — | 9 | 1 | no | — |
| 381 | C2×C3 | — | 9 | 1 | no | — |
| 382 | C2×C3 | — | 24 | 1 | no | — |
| 383 | C2×C3 | — | 24 | 1 | no | — |
| 384 | C2×C3 | — | 48 | 1 | no | — |
| 385 | C2×C3 | — | 72 | 1 | no | — |
| 386 | C2×C3 | #64242 | 1 | 1 | yes | characteristic |
| 387 | D3 | — | 6 | 1 | no | — |
| 388 | D3 | — | 6 | 1 | no | — |
| 389 | D3 | — | 6 | 1 | no | — |
| 390 | D3 | — | 6 | 1 | no | — |
| 391 | D3 | — | 8 | 1 | no | — |
| 392 | D3 | — | 24 | 1 | no | — |
| 393 | D3 | — | 24 | 1 | no | — |
| 394 | D3 | — | 48 | 1 | no | — |
| 395 | C22 | — | 9 | 1 | no | — |
| 396 | C22 | — | 12 | 1 | no | — |
| 397 | C22 | — | 36 | 1 | no | — |
| 398 | C22 | — | 36 | 1 | no | — |
| 399 | C22 | — | 36 | 1 | no | — |
| 400 | C22 | — | 108 | 1 | no | — |
| 401 | C22 | — | 108 | 1 | no | — |
| 402 | C4 | — | 2 | 1 | no | — |
| 403 | C4 | — | 9 | 1 | no | — |
| 404 | C4 | — | 18 | 1 | no | — |
| 405 | C4 | — | 27 | 2 | no | — |
| 406 | C4 | — | 54 | 1 | no | — |
| 407 | C4 | — | 108 | 1 | no | — |
| 408 | C4 | C2×D32⋊D3 | 1 | 1 | yes | characteristic |
| 409 | C3 | — | 2 | 1 | no | — |
| 410 | C3 | — | 2 | 1 | no | — |
| 411 | C3 | — | 4 | 1 | no | — |
| 412 | C3 | — | 4 | 1 | no | — |
| 413 | C3 | #10593476 | 1 | 1 | yes | characteristic, complemented |
| 414 | C2 | — | 9 | 1 | no | — |
| 415 | C2 | — | 9 | 1 | no | — |
| 416 | C2 | — | 24 | 1 | no | — |
| 417 | C2 | — | 72 | 1 | no | — |
| 418 | C2 | #11724332 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×C3⋊#157 | C2 | semidirect |
| 3. #11723708 | C2 | semidirect |
| 4. C3×#63940 | C2 | semidirect |
| 5. #11722763 | C2 | semidirect |
| 6. #11722758 | C2 | semidirect |
| 7. #11722757 | C2 | semidirect |
| 28. #63940 | D3 | semidirect |
| 40. C33×Q8 | D4 | semidirect |
| 45. C3×#634 | D4 | semidirect |
| 92. C3⋊#157 | SD16 | semidirect |
| 119. C32×Q8 | #67 | semidirect |
| 125. #634 | #67 | semidirect |
| 234. C33 | #460 | semidirect |
| 245. C3×Q8 | GO+(4,𝔽2) | semidirect |
| 357. C32 | #5163 | semidirect |
| 362. Q8 | D32⋊D3 | semidirect |
| 413. C3 | #10593476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊#157 | 2 |
| #11724315 | 2 |
| #11723708 | 2 |
| C3×#63940 | 2 |
| #11722763 | 2 |
| #11722758 | 2 |
| #11722757 | 2 |
| #10593476 | 3 |
| #5163 | 9 |