Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13078332 | C2 | semidirect |
| 2. #13078274 | C2 | semidirect |
| 3. C2×#10622204 | C2 | semidirect |
| 4. #13070344 | C2 | semidirect |
| 5. #13070243 | C2 | semidirect |
| 6. #13066715 | C2 | semidirect |
| 7. C11×#3414 | C2 | semidirect |
| 45. C2×C11×Q16 | D4 | semidirect |
| 49. C2×C11×D8 | D4 | semidirect |
| 76. C2×C11×C16 | D4 | semidirect |
| 82. #66883 | D4 | semidirect |
| 155. #3414 | D11 | semidirect |
| 269. C2×Q16 | C22⋊D11 | semidirect |
| 273. C2×D8 | C22⋊D11 | semidirect |
| 298. C2×C16 | C22⋊D11 | semidirect |
| 380. C11 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13078332 | 2 |
| #13078274 | 2 |
| C2×#10622204 | 2 |
| #13070344 | 2 |
| #13070243 | 2 |
| #13066715 | 2 |
| C11×#3414 | 2 |
| #13318 | 11 |