Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 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. #11763529 | C2 | semidirect |
| 3. #11763156 | C2 | semidirect |
| 4. #11763134 | C2 | semidirect |
| 5. #11763090 | C2 | semidirect |
| 6. #11763055 | C2 | semidirect |
| 7. #11763010 | C2 | semidirect |
| 8. #11762962 | C2 | semidirect |
| 9. C4×#63219 | C2 | semidirect |
| 10. #11762815 | C2 | semidirect |
| 11. C17×#436 | C2 | semidirect |
| 14. C2×M16×C17 | C22 | semidirect |
| 18. #10587612 | C22 | semidirect |
| 19. #10587610 | C22 | semidirect |
| 21. C2×#63219 | C22 | semidirect |
| 28. #10587555 | C22 | semidirect |
| 29. C4×Dic34 | C22 | semidirect |
| 30. C17×C4⋊C8 | C22 | semidirect |
| 31. C17×C22⋊C8 | C22 | semidirect |
| 32. C4×C8×C17 | C22 | semidirect |
| 35. #10587492 | C22 | semidirect |
| 36. #10587492 | C22 | semidirect |
| 37. #10587492 | C22 | semidirect |
| 38. #10587489 | C22 | semidirect |
| 39. #10587488 | C22 | semidirect |
| 40. #10587487 | C22 | semidirect |
| 139. #436 | D17 | semidirect |
| 151. C2×M16 | C2×D17 | semidirect |
| 167. C4⋊C8 | C2×D17 | semidirect |
| 174. C22⋊C8 | C2×D17 | semidirect |
| 175. C4×C8 | C2×D17 | semidirect |
| 176. C17 | #3324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763529 | 2 |
| D4×D68 | 2 |
| #11763156 | 2 |
| #11763134 | 2 |
| #11763090 | 2 |
| #11763055 | 2 |
| #11763010 | 2 |
| #11762962 | 2 |
| C4×#63219 | 2 |
| #11762815 | 2 |
| C17×#436 | 2 |
| #3324 | 17 |