Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
512 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 123 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. #13079272 | C2 | semidirect |
| 3. #13070834 | C2 | semidirect |
| 4. #13070793 | C2 | semidirect |
| 5. #13070792 | C2 | semidirect |
| 6. #13070694 | C2 | semidirect |
| 8. #13070510 | C2 | semidirect |
| 9. #13070508 | C2 | semidirect |
| 10. #13070431 | C2 | semidirect |
| 11. C11×#2214 | C2 | semidirect |
| 16. C11×#494 | C22 | semidirect |
| 21. #10622797 | C22 | semidirect |
| 32. #10622296 | C22 | semidirect |
| 33. C11×#364 | C22 | semidirect |
| 34. C11×#362 | C22 | semidirect |
| 36. #10622203 | C22 | semidirect |
| 39. #10622151 | C22 | semidirect |
| 40. #10622150 | C22 | semidirect |
| 41. #10622132 | C22 | semidirect |
| 42. #10622101 | C22 | semidirect |
| 158. #2214 | D11 | semidirect |
| 204. #494 | C2×D11 | semidirect |
| 222. #364 | C2×D11 | semidirect |
| 224. #362 | C2×D11 | semidirect |
| 357. C11 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079272 | 2 |
| #13077514 | 2 |
| #13070834 | 2 |
| #13070793 | 2 |
| #13070792 | 2 |
| #13070694 | 2 |
| #13070565 | 2 |
| #13070510 | 2 |
| #13070508 | 2 |
| #13070431 | 2 |
| C11×#2214 | 2 |
| #33693 | 11 |