Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
522 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 121 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. #13077417 | C2 | semidirect |
| 2. C2×#10622204 | C2 | semidirect |
| 3. #13070332 | C2 | semidirect |
| 4. #13069493 | C2 | semidirect |
| 5. #13066722 | C2 | semidirect |
| 6. #13066699 | C2 | semidirect |
| 12. C11×#509 | C4 | semidirect |
| 41. C2×C11×D8 | C2×C4 | semidirect |
| 57. C11×M32 | C2×C4 | semidirect |
| 92. C11×Q16 | C22⋊C4 | semidirect |
| 100. C11×D8 | C22⋊C4 | semidirect |
| 171. #509 | Dic11 | semidirect |
| 219. C2×D8 | C2×Dic11 | semidirect |
| 237. M32 | C2×Dic11 | semidirect |
| 275. Q16 | C22⋊Dic11 | semidirect |
| 283. D8 | C22⋊Dic11 | semidirect |
| 306. C11 | #13025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077417 | 2 |
| C2×#10622204 | 2 |
| #13070332 | 2 |
| #13069493 | 2 |
| #13066722 | 2 |
| #13066699 | 2 |
| C2×C11×#509 | 2 |
| #13025 | 11 |