Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 388 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. #11763519 | C2 | semidirect |
| 3. #11763159 | C2 | semidirect |
| 4. #11763138 | C2 | semidirect |
| 5. #11763100 | C2 | semidirect |
| 6. #11763064 | C2 | semidirect |
| 7. #11762970 | C2 | semidirect |
| 8. C4×#63230 | C2 | semidirect |
| 9. #11762886 | C2 | semidirect |
| 10. #11762809 | C2 | semidirect |
| 11. C17×#462 | C2 | semidirect |
| 128. #462 | D17 | semidirect |
| 167. C17 | #3331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763519 | 2 |
| #11763462 | 2 |
| #11763159 | 2 |
| #11763138 | 2 |
| #11763100 | 2 |
| #11763064 | 2 |
| #11762970 | 2 |
| C4×#63230 | 2 |
| #11762886 | 2 |
| #11762809 | 2 |
| C17×#462 | 2 |
| #3331 | 17 |