Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11763437 | C2 | semidirect |
| 3. #11763110 | C2 | semidirect |
| 4. #11763110 | C2 | semidirect |
| 5. #11763100 | C2 | semidirect |
| 6. #11763090 | C2 | semidirect |
| 7. #11762851 | C2 | semidirect |
| 8. #11762847 | C2 | semidirect |
| 11. C17×#424 | C2 | semidirect |
| 27. #10587556 | C22 | semidirect |
| 28. #10587555 | C22 | semidirect |
| 29. C17×C4⋊C8 | C22 | semidirect |
| 30. C17×C4⋊C8 | C22 | semidirect |
| 35. #10587489 | C22 | semidirect |
| 36. #10587489 | C22 | semidirect |
| 37. #10587489 | C22 | semidirect |
| 38. #10587488 | C22 | semidirect |
| 39. #10587488 | C22 | semidirect |
| 40. #10587488 | C22 | semidirect |
| 46. C2×D68 | Q8 | semidirect |
| 128. #424 | D17 | semidirect |
| 159. C4⋊C8 | C2×D17 | semidirect |
| 160. C4⋊C8 | C2×D17 | semidirect |
| 165. C17 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763437 | 2 |
| #11763283 | 2 |
| #11763110 | 2 |
| #11763100 | 2 |
| #11763090 | 2 |
| #11762851 | 2 |
| #11762847 | 2 |
| #11762815 | 2 |
| C2×#10587492 | 2 |
| C17×#424 | 2 |
| #3081 | 17 |