Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763433 | C2 | semidirect |
| 2. #11763193 | C2 | semidirect |
| 3. #11763171 | C2 | semidirect |
| 4. #11763056 | C2 | semidirect |
| 5. #11763051 | C2 | semidirect |
| 7. #11762908 | C2 | semidirect |
| 8. #11762903 | C2 | semidirect |
| 9. #11762891 | C2 | semidirect |
| 10. #11762763 | C2 | semidirect |
| 11. C17×#500 | C2 | semidirect |
| 114. #500 | D17 | semidirect |
| 156. C17 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763433 | 2 |
| #11763193 | 2 |
| #11763171 | 2 |
| #11763056 | 2 |
| #11763051 | 2 |
| #11763046 | 2 |
| #11762908 | 2 |
| #11762903 | 2 |
| #11762891 | 2 |
| #11762763 | 2 |
| C17×#500 | 2 |
| #3175 | 17 |