Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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. #11763529 | C2 | semidirect |
| 3. #11763156 | C2 | semidirect |
| 4. #11763134 | C2 | semidirect |
| 5. #11763095 | C2 | semidirect |
| 6. #11763038 | C2 | semidirect |
| 7. #11763010 | C2 | semidirect |
| 8. #11762973 | C2 | semidirect |
| 9. C4×Dic68 | C2 | semidirect |
| 10. #11762806 | C2 | semidirect |
| 11. C8×D4×C17 | C2 | semidirect |
| 132. C8×D4 | D17 | semidirect |
| 168. C17 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763529 | 2 |
| #11763480 | 2 |
| #11763156 | 2 |
| #11763134 | 2 |
| #11763095 | 2 |
| #11763038 | 2 |
| #11763010 | 2 |
| #11762973 | 2 |
| C4×Dic68 | 2 |
| #11762806 | 2 |
| C8×D4×C17 | 2 |
| #3304 | 17 |