Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11763363 | C2 | semidirect |
| 3. #11763101 | C2 | semidirect |
| 4. #11763088 | C2 | semidirect |
| 5. #11763058 | C2 | semidirect |
| 6. #11763056 | C2 | semidirect |
| 7. #11763013 | C2 | semidirect |
| 8. #11763010 | C2 | semidirect |
| 9. #11763009 | C2 | semidirect |
| 10. #11762831 | C2 | semidirect |
| 11. C17×#477 | C2 | semidirect |
| 136. #477 | D17 | semidirect |
| 180. C17 | #3254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763363 | 2 |
| #11763360 | 2 |
| #11763101 | 2 |
| #11763088 | 2 |
| #11763058 | 2 |
| #11763056 | 2 |
| #11763013 | 2 |
| #11763010 | 2 |
| #11763009 | 2 |
| #11762831 | 2 |
| C17×#477 | 2 |
| #3254 | 17 |