Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11763174 | C2 | semidirect |
| 4. #11763169 | C2 | semidirect |
| 5. #11763164 | C2 | semidirect |
| 6. #11763156 | C2 | semidirect |
| 7. #11762815 | C2 | semidirect |
| 8. #11762811 | C2 | semidirect |
| 9. #11762806 | C2 | semidirect |
| 10. C2×#10587492 | C2 | semidirect |
| 11. C17×#405 | C2 | semidirect |
| 27. #10587556 | C22 | semidirect |
| 28. #10587555 | C22 | semidirect |
| 29. C17×#97 | C22 | semidirect |
| 30. C4×C8×C17 | C22 | semidirect |
| 35. #10587492 | C22 | semidirect |
| 36. #10587492 | C22 | semidirect |
| 37. #10587492 | C22 | semidirect |
| 38. #10587487 | C22 | semidirect |
| 39. #10587487 | C22 | semidirect |
| 40. #10587487 | C22 | semidirect |
| 140. #405 | D17 | semidirect |
| 174. #97 | C2×D17 | semidirect |
| 175. C4×C8 | C2×D17 | semidirect |
| 176. C17 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763437 | 2 |
| #11763378 | 2 |
| #11763174 | 2 |
| #11763169 | 2 |
| #11763164 | 2 |
| #11763156 | 2 |
| #11762815 | 2 |
| #11762811 | 2 |
| #11762806 | 2 |
| C2×#10587492 | 2 |
| C17×#405 | 2 |
| #3136 | 17 |