Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
591 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 591 conjugacy classes of subgroups — too many to draw. Only its 70 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⋊#6296 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10620157 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×#6295 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#6289 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×Dic3×C3⋊D3 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #89042 | — | 3 | 1 | no | maximal |
| 7 | #88960 | — | 3 | 2 | no | maximal |
| 8 | #88959 | — | 3 | 1 | no | maximal |
| 9 | C2×C3×C3⋊(C3⋊D3) | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C32×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 11 | C3×C3⋊(C3⋊Dic3) | C22 | 1 | 2 | yes | — |
| 12 | C32×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 13 | C33×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×C4×C3⋊D3 | — | 3 | 2 | no | — |
| 15 | C3×C4×C3⋊D3 | — | 3 | 1 | no | — |
| 16 | #6296 | — | 3 | 1 | no | — |
| 17 | #6296 | — | 3 | 1 | no | — |
| 18 | #6296 | — | 6 | 1 | no | — |
| 19 | #6295 | — | 3 | 2 | no | — |
| 20 | #6295 | — | 3 | 2 | no | — |
| 21 | #6295 | — | 6 | 2 | no | — |
| 22 | #6295 | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | #6293 | — | 3 | 2 | no | — |
| 24 | #6291 | — | 3 | 2 | no | — |
| 25 | #6290 | — | 3 | 2 | no | — |
| 26 | #6289 | D3 | 1 | 1 | yes | characteristic, complemented |
| 27 | Dic3×C3⋊D3 | D3 | 1 | 2 | yes | complemented |
| 28 | C3×#626 | — | 3 | 2 | no | — |
| 29 | C3×#625 | — | 3 | 1 | no | — |
| 30 | C3×#624 | — | 3 | 2 | no | — |
| 31 | C3×#624 | — | 6 | 1 | no | — |
| 32 | C3×D3×Dic3 | — | 3 | 2 | no | — |
| 33 | C3×D3×Dic3 | — | 3 | 2 | no | — |
| 34 | C3×D3×Dic3 | — | 6 | 2 | no | — |
| 35 | C2×C34 | C23 | 1 | 1 | yes | characteristic |
| 36 | C3×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 37 | C32×C3⋊D3 | — | 2 | 2 | no | — |
| 38 | #3804 | — | 9 | 2 | no | — |
| 39 | #3798 | — | 9 | 1 | no | — |
| 40 | #3798 | — | 9 | 2 | no | — |
| 41 | #3795 | — | 9 | 1 | no | — |
| 42 | C2×C3⋊(C3⋊D3) | C2×D3 | 1 | 1 | yes | characteristic |
| 43 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 44 | C2×C3×C3⋊D3 | — | 3 | 2 | no | — |
| 45 | C2×C3×C3⋊D3 | — | 3 | 1 | no | — |
| 46 | C2×C3×C3⋊D3 | — | 6 | 1 | no | — |
| 47 | C2×C3×C3⋊D3 | — | 6 | 2 | no | — |
| 48 | C2×C3×C3⋊D3 | — | 12 | 1 | no | — |
| 49 | C2×C3×C3⋊D3 | C2×D3 | 1 | 2 | yes | — |
| 50 | C2×C3×C3⋊D3 | C2×D3 | 1 | 2 | yes | — |
| 51 | C2×C32×D3 | — | 3 | 2 | no | — |
| 52 | C2×C32×D3 | — | 3 | 2 | no | — |
| 53 | C2×C32×D3 | — | 6 | 2 | no | — |
| 54 | C33×C4 | — | 3 | 1 | no | — |
| 55 | C3⋊(C3⋊Dic3) | C2×D3 | 1 | 2 | yes | — |
| 56 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 57 | C3×C3⋊Dic3 | — | 3 | 2 | no | — |
| 58 | C3×C3⋊Dic3 | — | 3 | 2 | no | — |
| 59 | C3×C3⋊Dic3 | — | 3 | 2 | no | — |
| 60 | C3×C3⋊Dic3 | — | 6 | 2 | no | — |
| 61 | C3×C3⋊Dic3 | — | 6 | 2 | no | — |
| 62 | C3×C3⋊Dic3 | — | 6 | 2 | no | — |
| 63 | C3×C3⋊Dic3 | — | 12 | 2 | no | — |
| 64 | C3×C3⋊Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 65 | C3×C3⋊Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 66 | C32×Dic3 | — | 2 | 2 | no | — |
| 67 | C32×Dic3 | — | 2 | 1 | no | — |
| 68 | C32×Dic3 | — | 3 | 2 | no | — |
| 69 | C32×Dic3 | — | 4 | 1 | no | — |
| 70 | C32×Dic3 | — | 6 | 1 | no | — |
| 71 | C32×Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 72 | C32×Dic3 | C2×D3 | 1 | 2 | yes | — |
| 73 | C34 | #41 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 74 | #638 | — | 9 | 2 | no | — |
| 75 | C4×C3⋊D3 | — | 3 | 2 | no | — |
| 76 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 77 | #634 | — | 9 | 1 | no | — |
| 78 | C3×#67 | — | 9 | 2 | no | — |
| 79 | C2×C3×Dic3 | — | 9 | 2 | no | — |
| 80 | C3×D12 | — | 9 | 1 | no | — |
| 81 | C3×C4×D3 | — | 9 | 2 | no | — |
| 82 | C3×C4×D3 | — | 9 | 2 | no | — |
| 83 | C3×C4×D3 | — | 9 | 2 | no | — |
| 84 | C3×C4×D3 | — | 9 | 1 | no | — |
| 85 | C3×C4×D3 | — | 18 | 1 | no | — |
| 86 | C3×C4×D3 | — | 18 | 2 | no | — |
| 87 | #627 | — | 9 | 2 | no | — |
| 88 | #627 | — | 9 | 2 | no | — |
| 89 | #627 | — | 9 | 1 | no | — |
| 90 | #627 | — | 18 | 2 | no | — |
| 91 | #626 | — | 3 | 2 | no | — |
| 92 | #626 | — | 9 | 2 | no | — |
| 93 | #626 | — | 9 | 2 | no | — |
| 94 | #626 | — | 9 | 2 | no | — |
| 95 | #626 | — | 18 | 2 | no | — |
| 96 | #625 | — | 3 | 1 | no | — |
| 97 | #625 | — | 9 | 2 | no | — |
| 98 | #625 | — | 9 | 2 | no | — |
| 99 | #625 | — | 18 | 2 | no | — |
| 100 | #624 | — | 3 | 2 | no | — |
| 101 | #624 | — | 6 | 1 | no | — |
| 102 | D3×Dic3 | — | 3 | 2 | no | — |
| 103 | D3×Dic3 | — | 3 | 2 | no | — |
| 104 | D3×Dic3 | — | 6 | 2 | no | — |
| 105 | C2×C33 | — | 2 | 1 | no | — |
| 106 | C2×C33 | — | 2 | 2 | no | — |
| 107 | C2×C33 | — | 2 | 1 | no | — |
| 108 | C2×C33 | — | 2 | 2 | no | — |
| 109 | C2×C33 | — | 4 | 1 | no | — |
| 110 | C2×C33 | — | 4 | 2 | no | — |
| 111 | C2×C33 | — | 4 | 1 | no | — |
| 112 | C2×C33 | — | 8 | 1 | no | — |
| 113 | C2×C33 | C22×D3 | 1 | 2 | yes | — |
| 114 | C2×C33 | C22×D3 | 1 | 1 | yes | characteristic |
| 115 | C2×C33 | C22×D3 | 1 | 1 | yes | characteristic |
| 116 | C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 117 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 118 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 119 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 120 | C3×C3⋊D3 | — | 6 | 1 | no | — |
| 121 | C3×C3⋊D3 | — | 6 | 2 | no | — |
| 122 | C3×C3⋊D3 | — | 6 | 2 | no | — |
| 123 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 124 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 125 | C32×D3 | — | 6 | 4 | no | — |
| 126 | C32×D3 | — | 6 | 2 | no | — |
| 127 | C32×D3 | — | 6 | 2 | no | — |
| 128 | #237 | — | 27 | 1 | no | — |
| 129 | #235 | — | 27 | 1 | no | — |
| 130 | #235 | — | 27 | 2 | no | — |
| 131 | C22×C32 | — | 9 | 2 | no | — |
| 132 | C2×C3⋊D3 | — | 3 | 2 | no | — |
| 133 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 134 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 135 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 136 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 137 | C2×C3⋊D3 | D32 | 1 | 2 | yes | — |
| 138 | C2×C3×D3 | — | 3 | 2 | no | — |
| 139 | C2×C3×D3 | — | 3 | 2 | no | — |
| 140 | C2×C3×D3 | — | 3 | 2 | no | — |
| 141 | C2×C3×D3 | — | 3 | 2 | no | — |
| 142 | C2×C3×D3 | — | 6 | 2 | no | — |
| 143 | C2×C3×D3 | — | 6 | 2 | no | — |
| 144 | C2×C3×D3 | — | 6 | 2 | no | — |
| 145 | C2×C3×D3 | — | 6 | 2 | no | — |
| 146 | C2×C3×D3 | — | 9 | 1 | no | — |
| 147 | C2×C3×D3 | — | 9 | 2 | no | — |
| 148 | C2×C3×D3 | — | 12 | 2 | no | — |
| 149 | C2×C3×D3 | — | 18 | 1 | no | — |
| 150 | C2×C3×D3 | — | 18 | 2 | no | — |
| 151 | C2×C3×D3 | — | 36 | 1 | no | — |
| 152 | C32×C4 | — | 3 | 1 | no | — |
| 153 | C32×C4 | — | 3 | 2 | no | — |
| 154 | C32×C4 | — | 6 | 1 | no | — |
| 155 | C32×C4 | — | 6 | 2 | no | — |
| 156 | C32×C4 | — | 9 | 1 | no | — |
| 157 | C32×C4 | — | 12 | 1 | no | — |
| 158 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 159 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 160 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 161 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 162 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 163 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 164 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 165 | C3⋊Dic3 | D32 | 1 | 1 | yes | characteristic |
| 166 | C3×Dic3 | — | 2 | 2 | no | — |
| 167 | C3×Dic3 | — | 2 | 1 | no | — |
| 168 | C3×Dic3 | — | 3 | 2 | no | — |
| 169 | C3×Dic3 | — | 3 | 2 | no | — |
| 170 | C3×Dic3 | — | 4 | 1 | no | — |
| 171 | C3×Dic3 | — | 6 | 2 | no | — |
| 172 | C3×Dic3 | — | 6 | 1 | no | — |
| 173 | C3×Dic3 | — | 6 | 1 | no | — |
| 174 | C3×Dic3 | — | 9 | 2 | no | — |
| 175 | C3×Dic3 | — | 9 | 2 | no | — |
| 176 | C3×Dic3 | — | 9 | 2 | no | — |
| 177 | C3×Dic3 | — | 12 | 1 | no | — |
| 178 | C3×Dic3 | — | 18 | 2 | no | — |
| 179 | C3×Dic3 | — | 18 | 2 | no | — |
| 180 | C3×Dic3 | — | 18 | 2 | no | — |
| 181 | C3×Dic3 | — | 36 | 2 | no | — |
| 182 | C3×Dic3 | D32 | 1 | 1 | yes | characteristic |
| 183 | C3×Dic3 | D32 | 1 | 2 | yes | — |
| 184 | C33 | — | 2 | 1 | no | — |
| 185 | C33 | — | 2 | 2 | no | — |
| 186 | C33 | — | 2 | 1 | no | — |
| 187 | C33 | — | 2 | 2 | no | — |
| 188 | C33 | — | 4 | 1 | no | — |
| 189 | C33 | — | 4 | 2 | no | — |
| 190 | C33 | — | 4 | 1 | no | — |
| 191 | C33 | — | 8 | 1 | no | — |
| 192 | C33 | #235 | 1 | 1 | yes | characteristic, complemented |
| 193 | C33 | #235 | 1 | 2 | yes | complemented |
| 194 | C33 | #237 | 1 | 1 | yes | characteristic, complemented |
| 195 | C3×D4 | — | 27 | 1 | no | — |
| 196 | C2×C3×C4 | — | 27 | 1 | no | — |
| 197 | C2×C3×C4 | — | 27 | 2 | no | — |
| 198 | #67 | — | 9 | 2 | no | — |
| 199 | #67 | — | 27 | 2 | no | — |
| 200 | #67 | — | 27 | 2 | no | — |
| 201 | #67 | — | 27 | 2 | no | — |
| 202 | #67 | — | 54 | 2 | no | — |
| 203 | C2×Dic3 | — | 9 | 2 | no | — |
| 204 | D12 | — | 9 | 1 | no | — |
| 205 | D12 | — | 27 | 2 | no | — |
| 206 | C4×D3 | — | 9 | 2 | no | — |
| 207 | C4×D3 | — | 9 | 2 | no | — |
| 208 | C4×D3 | — | 9 | 2 | no | — |
| 209 | C4×D3 | — | 9 | 1 | no | — |
| 210 | C4×D3 | — | 18 | 1 | no | — |
| 211 | C4×D3 | — | 18 | 2 | no | — |
| 212 | Dic6 | — | 27 | 2 | no | — |
| 213 | Dic6 | — | 27 | 1 | no | — |
| 214 | Dic6 | — | 27 | 1 | no | — |
| 215 | Dic6 | — | 54 | 1 | no | — |
| 216 | C2×C32 | — | 2 | 2 | no | — |
| 217 | C2×C32 | — | 2 | 1 | no | — |
| 218 | C2×C32 | — | 2 | 2 | no | — |
| 219 | C2×C32 | — | 2 | 2 | no | — |
| 220 | C2×C32 | — | 2 | 2 | no | — |
| 221 | C2×C32 | — | 2 | 1 | no | — |
| 222 | C2×C32 | — | 2 | 2 | no | — |
| 223 | C2×C32 | — | 4 | 2 | no | — |
| 224 | C2×C32 | — | 4 | 1 | no | — |
| 225 | C2×C32 | — | 4 | 1 | no | — |
| 226 | C2×C32 | — | 4 | 1 | no | — |
| 227 | C2×C32 | — | 4 | 2 | no | — |
| 228 | C2×C32 | — | 4 | 2 | no | — |
| 229 | C2×C32 | — | 4 | 1 | no | — |
| 230 | C2×C32 | — | 4 | 1 | no | — |
| 231 | C2×C32 | — | 8 | 1 | no | — |
| 232 | C2×C32 | — | 8 | 1 | no | — |
| 233 | C2×C32 | — | 8 | 2 | no | — |
| 234 | C2×C32 | — | 8 | 2 | no | — |
| 235 | C2×C32 | — | 8 | 1 | no | — |
| 236 | C2×C32 | — | 18 | 2 | no | — |
| 237 | C2×C32 | C2×D32 | 1 | 1 | yes | characteristic |
| 238 | C2×C32 | C2×D32 | 1 | 2 | yes | — |
| 239 | C2×C32 | C2×D32 | 1 | 2 | yes | — |
| 240 | C2×C32 | C2×D32 | 1 | 1 | yes | characteristic |
| 241 | C3⋊D3 | — | 2 | 2 | no | — |
| 242 | C3⋊D3 | — | 6 | 1 | no | — |
| 243 | C3⋊D3 | — | 6 | 2 | no | — |
| 244 | C3⋊D3 | — | 6 | 2 | no | — |
| 245 | C3⋊D3 | — | 12 | 2 | no | — |
| 246 | C3⋊D3 | — | 12 | 2 | no | — |
| 247 | C3×D3 | — | 6 | 4 | no | — |
| 248 | C3×D3 | — | 6 | 4 | no | — |
| 249 | C3×D3 | — | 6 | 2 | no | — |
| 250 | C3×D3 | — | 6 | 2 | no | — |
| 251 | C3×D3 | — | 6 | 2 | no | — |
| 252 | C3×D3 | — | 6 | 2 | no | — |
| 253 | C3×D3 | — | 12 | 2 | no | — |
| 254 | C3×D3 | — | 12 | 2 | no | — |
| 255 | C3×D3 | — | 12 | 4 | no | — |
| 256 | C3×D3 | — | 18 | 2 | no | — |
| 257 | C3×D3 | — | 18 | 1 | no | — |
| 258 | C3×D3 | — | 18 | 2 | no | — |
| 259 | C3×D3 | — | 36 | 2 | no | — |
| 260 | C3×D3 | — | 36 | 2 | no | — |
| 261 | #41 | — | 81 | 1 | no | Sylow |
| 262 | C22×C3 | — | 9 | 2 | no | — |
| 263 | C22×C3 | — | 9 | 2 | no | — |
| 264 | C22×C3 | — | 18 | 2 | no | — |
| 265 | C22×C3 | — | 27 | 1 | no | — |
| 266 | C2×D3 | — | 3 | 2 | no | — |
| 267 | C2×D3 | — | 3 | 2 | no | — |
| 268 | C2×D3 | — | 6 | 2 | no | — |
| 269 | C2×D3 | — | 9 | 2 | no | — |
| 270 | C2×D3 | — | 9 | 1 | no | — |
| 271 | C2×D3 | — | 18 | 1 | no | — |
| 272 | C2×D3 | — | 18 | 2 | no | — |
| 273 | C2×D3 | — | 36 | 1 | no | — |
| 274 | C3×C4 | — | 3 | 1 | no | — |
| 275 | C3×C4 | — | 3 | 2 | no | — |
| 276 | C3×C4 | — | 6 | 1 | no | — |
| 277 | C3×C4 | — | 6 | 2 | no | — |
| 278 | C3×C4 | — | 9 | 1 | no | — |
| 279 | C3×C4 | — | 9 | 1 | no | — |
| 280 | C3×C4 | — | 12 | 1 | no | — |
| 281 | C3×C4 | — | 18 | 1 | no | — |
| 282 | C3×C4 | — | 27 | 2 | no | — |
| 283 | Dic3 | — | 3 | 2 | no | — |
| 284 | Dic3 | — | 6 | 1 | no | — |
| 285 | Dic3 | — | 9 | 2 | no | — |
| 286 | Dic3 | — | 9 | 2 | no | — |
| 287 | Dic3 | — | 9 | 2 | no | — |
| 288 | Dic3 | — | 18 | 2 | no | — |
| 289 | Dic3 | — | 18 | 2 | no | — |
| 290 | Dic3 | — | 18 | 2 | no | — |
| 291 | Dic3 | — | 36 | 2 | no | — |
| 292 | Dic3 | #1113 | 1 | 1 | yes | characteristic |
| 293 | C32 | — | 2 | 2 | no | — |
| 294 | C32 | — | 2 | 1 | no | — |
| 295 | C32 | — | 2 | 2 | no | — |
| 296 | C32 | — | 2 | 2 | no | — |
| 297 | C32 | — | 2 | 2 | no | — |
| 298 | C32 | — | 2 | 2 | no | — |
| 299 | C32 | — | 2 | 1 | no | — |
| 300 | C32 | — | 4 | 1 | no | — |
| 301 | C32 | — | 4 | 2 | no | — |
| 302 | C32 | — | 4 | 1 | no | — |
| 303 | C32 | — | 4 | 2 | no | — |
| 304 | C32 | — | 4 | 1 | no | — |
| 305 | C32 | — | 4 | 1 | no | — |
| 306 | C32 | — | 4 | 2 | no | — |
| 307 | C32 | — | 4 | 1 | no | — |
| 308 | C32 | — | 8 | 2 | no | — |
| 309 | C32 | — | 8 | 1 | no | — |
| 310 | C32 | — | 8 | 2 | no | — |
| 311 | C32 | — | 8 | 1 | no | — |
| 312 | C32 | — | 8 | 1 | no | — |
| 313 | C32 | #3795 | 1 | 1 | yes | characteristic, complemented |
| 314 | C32 | #3798 | 1 | 1 | yes | characteristic, complemented |
| 315 | C32 | #3798 | 1 | 2 | yes | complemented |
| 316 | C32 | #3804 | 1 | 2 | yes | complemented |
| 317 | Q8 | — | 81 | 1 | no | — |
| 318 | D4 | — | 27 | 1 | no | — |
| 319 | D4 | — | 81 | 2 | no | — |
| 320 | C2×C4 | — | 27 | 1 | no | — |
| 321 | C2×C4 | — | 27 | 2 | no | — |
| 322 | C2×C3 | — | 2 | 1 | no | — |
| 323 | C2×C3 | — | 2 | 1 | no | — |
| 324 | C2×C3 | — | 2 | 2 | no | — |
| 325 | C2×C3 | — | 2 | 2 | no | — |
| 326 | C2×C3 | — | 4 | 2 | no | — |
| 327 | C2×C3 | — | 4 | 1 | no | — |
| 328 | C2×C3 | — | 4 | 1 | no | — |
| 329 | C2×C3 | — | 8 | 1 | no | — |
| 330 | C2×C3 | — | 18 | 2 | no | — |
| 331 | C2×C3 | — | 18 | 2 | no | — |
| 332 | C2×C3 | — | 36 | 2 | no | — |
| 333 | C2×C3 | — | 54 | 1 | no | — |
| 334 | C2×C3 | D33 | 1 | 1 | yes | characteristic |
| 335 | C2×C3 | D33 | 1 | 2 | yes | — |
| 336 | C2×C3 | C2×#1113 | 1 | 1 | yes | characteristic |
| 337 | D3 | — | 6 | 4 | no | — |
| 338 | D3 | — | 6 | 2 | no | — |
| 339 | D3 | — | 6 | 2 | no | — |
| 340 | D3 | — | 18 | 2 | no | — |
| 341 | D3 | — | 18 | 2 | no | — |
| 342 | D3 | — | 18 | 1 | no | — |
| 343 | D3 | — | 36 | 2 | no | — |
| 344 | D3 | — | 36 | 2 | no | — |
| 345 | C22 | — | 9 | 2 | no | — |
| 346 | C22 | — | 27 | 1 | no | — |
| 347 | C4 | — | 3 | 1 | no | — |
| 348 | C4 | — | 9 | 1 | no | — |
| 349 | C4 | — | 27 | 2 | no | — |
| 350 | C3 | — | 2 | 2 | no | — |
| 351 | C3 | — | 2 | 1 | no | — |
| 352 | C3 | — | 2 | 2 | no | — |
| 353 | C3 | — | 2 | 1 | no | — |
| 354 | C3 | — | 4 | 1 | no | — |
| 355 | C3 | — | 4 | 2 | no | — |
| 356 | C3 | — | 4 | 1 | no | — |
| 357 | C3 | — | 8 | 1 | no | — |
| 358 | C3 | #88959 | 1 | 1 | yes | characteristic, complemented |
| 359 | C3 | #88960 | 1 | 2 | yes | complemented |
| 360 | C3 | #89042 | 1 | 1 | yes | characteristic, complemented |
| 361 | C2 | — | 18 | 2 | no | — |
| 362 | C2 | — | 54 | 1 | no | — |
| 363 | C2 | D3×#1113 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#1113 |
| commutator, Fitting, socle, cosocle | C2×C34 | C23 |
| hypocenter | C34 | #41 |
| LCS | G ▷ C2×C34 ▷ C34 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊#6296 | C2 | semidirect |
| 2. #10620157 | C2 | semidirect |
| 3. C3×#6295 | C2 | semidirect |
| 4. C3×#6289 | C2 | semidirect |
| 5. C3×Dic3×C3⋊D3 | C2 | semidirect |
| 22. #6295 | D3 | semidirect |
| 26. #6289 | D3 | semidirect |
| 27. Dic3×C3⋊D3 | D3 | semidirect |
| 73. C34 | #41 | semidirect |
| 192. C33 | #235 | semidirect |
| 193. C33 | #235 | semidirect |
| 194. C33 | #237 | semidirect |
| 313. C32 | #3795 | semidirect |
| 314. C32 | #3798 | semidirect |
| 315. C32 | #3798 | semidirect |
| 316. C32 | #3804 | semidirect |
| 358. C3 | #88959 | semidirect |
| 359. C3 | #88960 | semidirect |
| 360. C3 | #89042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊#6296 | 2 |
| #10620157 | 2 |
| C3×#6295 | 2 |
| C3×#6289 | 2 |
| C3×Dic3×C3⋊D3 | 2 |
| #89042 | 3 |
| #88960 | 3 |
| #88959 | 3 |