Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 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. #11763542 | C2 | semidirect |
| 2. #11763193 | C2 | semidirect |
| 3. #11763192 | C2 | semidirect |
| 5. #11763024 | C2 | semidirect |
| 6. #11763023 | C2 | semidirect |
| 7. #11763008 | C2 | semidirect |
| 8. C8×Dic34 | C2 | semidirect |
| 9. #11762903 | C2 | semidirect |
| 10. #11762891 | C2 | semidirect |
| 11. C4×D8×C17 | C2 | semidirect |
| 126. C4×D8 | D17 | semidirect |
| 159. C17 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763542 | 2 |
| #11763193 | 2 |
| #11763192 | 2 |
| #11763184 | 2 |
| #11763024 | 2 |
| #11763023 | 2 |
| #11763008 | 2 |
| C8×Dic34 | 2 |
| #11762903 | 2 |
| #11762891 | 2 |
| C4×D8×C17 | 2 |
| #3396 | 17 |