Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #11763157 | C2 | semidirect |
| 3. #11763122 | C2 | semidirect |
| 4. #11763101 | C2 | semidirect |
| 5. #11763057 | C2 | semidirect |
| 6. #11763009 | C2 | semidirect |
| 7. #11762969 | C2 | semidirect |
| 8. C4×#63231 | C2 | semidirect |
| 9. #11762887 | C2 | semidirect |
| 10. #11762808 | C2 | semidirect |
| 11. C17×#554 | C2 | semidirect |
| 124. #554 | D17 | semidirect |
| 169. C17 | #3333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763480 | 2 |
| #11763157 | 2 |
| #11763122 | 2 |
| #11763101 | 2 |
| #11763057 | 2 |
| #11763009 | 2 |
| #11762969 | 2 |
| C4×#63231 | 2 |
| #11762887 | 2 |
| #11762808 | 2 |
| C17×#554 | 2 |
| #3333 | 17 |