Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 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. C2×#10587598 | C2 | semidirect |
| 2. C2×Q16×D17 | C2 | semidirect |
| 3. #11763467 | C2 | semidirect |
| 4. #11763047 | C2 | semidirect |
| 5. #11763042 | C2 | semidirect |
| 6. #11763028 | C2 | semidirect |
| 7. #11762968 | C2 | semidirect |
| 8. #11762946 | C2 | semidirect |
| 9. C4×Dic68 | C2 | semidirect |
| 10. C8×D68 | C2 | semidirect |
| 11. C17×#495 | C2 | semidirect |
| 77. Dic68 | D4 | semidirect |
| 121. C2×D17 | #135 | semidirect |
| 134. #495 | D17 | semidirect |
| 177. C17 | #3285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587598 | 2 |
| C2×Q16×D17 | 2 |
| #11763467 | 2 |
| #11763047 | 2 |
| #11763042 | 2 |
| #11763028 | 2 |
| #11762968 | 2 |
| #11762946 | 2 |
| C4×Dic68 | 2 |
| C8×D68 | 2 |
| C17×#495 | 2 |
| #3285 | 17 |