Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 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. #11763357 | C2 | semidirect |
| 2. #11763356 | C2 | semidirect |
| 3. #11763100 | C2 | semidirect |
| 4. #11763099 | C2 | semidirect |
| 5. #11763097 | C2 | semidirect |
| 6. #11763061 | C2 | semidirect |
| 7. #11763059 | C2 | semidirect |
| 8. #11763002 | C2 | semidirect |
| 9. #11763001 | C2 | semidirect |
| 10. #11762831 | C2 | semidirect |
| 11. C17×#459 | C2 | semidirect |
| 153. #459 | D17 | semidirect |
| 193. C17 | #3253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763357 | 2 |
| #11763356 | 2 |
| #11763100 | 2 |
| #11763099 | 2 |
| #11763097 | 2 |
| #11763061 | 2 |
| #11763059 | 2 |
| #11763002 | 2 |
| #11763001 | 2 |
| #11762831 | 2 |
| C17×#459 | 2 |
| #3253 | 17 |