Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 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. #11763531 | C2 | semidirect |
| 4. #11763187 | C2 | semidirect |
| 5. #11763034 | C2 | semidirect |
| 6. #11763031 | C2 | semidirect |
| 7. #11763013 | C2 | semidirect |
| 8. C8×Dic34 | C2 | semidirect |
| 9. #11762903 | C2 | semidirect |
| 11. C4×Q16×C17 | C2 | semidirect |
| 120. C4×Q16 | D17 | semidirect |
| 153. C17 | #3393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763531 | 2 |
| #11763194 | 2 |
| #11763193 | 2 |
| #11763187 | 2 |
| #11763034 | 2 |
| #11763031 | 2 |
| #11763013 | 2 |
| C8×Dic34 | 2 |
| #11762903 | 2 |
| #11762891 | 2 |
| C4×Q16×C17 | 2 |
| #3393 | 17 |