Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763624 | C2 | semidirect |
| 2. #11763623 | C2 | semidirect |
| 3. #11763187 | C2 | semidirect |
| 4. #11763084 | C2 | semidirect |
| 5. #11763082 | C2 | semidirect |
| 6. #11763081 | C2 | semidirect |
| 7. #11762992 | C2 | semidirect |
| 8. #11762990 | C2 | semidirect |
| 9. #11762926 | C2 | semidirect |
| 10. #11762924 | C2 | semidirect |
| 11. C17×#578 | C2 | semidirect |
| 144. #578 | D17 | semidirect |
| 191. C17 | #3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763624 | 2 |
| #11763623 | 2 |
| #11763187 | 2 |
| #11763084 | 2 |
| #11763082 | 2 |
| #11763081 | 2 |
| #11762992 | 2 |
| #11762990 | 2 |
| #11762926 | 2 |
| #11762924 | 2 |
| C17×#578 | 2 |
| #3293 | 17 |