Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763366 | C2 | semidirect |
| 3. #11763117 | C2 | semidirect |
| 4. #11763095 | C2 | semidirect |
| 5. #11763090 | C2 | semidirect |
| 6. #11763050 | C2 | semidirect |
| 8. #11763032 | C2 | semidirect |
| 9. #11763020 | C2 | semidirect |
| 10. #11763015 | C2 | semidirect |
| 11. C2×C17×C4⋊C8 | C2 | semidirect |
| 139. C2×C4⋊C8 | D17 | semidirect |
| 176. C17 | #3248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| #11763343 | 2 |
| #11763117 | 2 |
| #11763095 | 2 |
| #11763090 | 2 |
| #11763050 | 2 |
| #11763038 | 2 |
| #11763032 | 2 |
| #11763020 | 2 |
| #11763015 | 2 |
| C2×C17×C4⋊C8 | 2 |
| #3248 | 17 |