Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763380 | C2 | semidirect |
| 3. #11763151 | C2 | semidirect |
| 4. #11763134 | C2 | semidirect |
| 5. #11763055 | C2 | semidirect |
| 6. #11763038 | C2 | semidirect |
| 7. #11762962 | C2 | semidirect |
| 8. #11762950 | C2 | semidirect |
| 9. C17×#408 | C2 | semidirect |
| 12. C22×Dic34 | C22 | semidirect |
| 13. C2×M16×C17 | C22 | semidirect |
| 14. C22×C8×C17 | C22 | semidirect |
| 26. #10587612 | C22 | semidirect |
| 28. #10587610 | C22 | semidirect |
| 32. C17×C22⋊C8 | C22 | semidirect |
| 35. #10587489 | C22 | semidirect |
| 36. #10587488 | C22 | semidirect |
| 37. #10587487 | C22 | semidirect |
| 38. #10587487 | C22 | semidirect |
| 140. #408 | D17 | semidirect |
| 152. C2×M16 | C2×D17 | semidirect |
| 153. C22×C8 | C2×D17 | semidirect |
| 175. C22⋊C8 | C2×D17 | semidirect |
| 176. C17 | #3200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763380 | 2 |
| #11763373 | 2 |
| #11763151 | 2 |
| #11763134 | 2 |
| #11763055 | 2 |
| #11763038 | 2 |
| #11762962 | 2 |
| #11762950 | 2 |
| C17×#408 | 2 |
| #3200 | 17 |