Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
588 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11763807 | C2 | semidirect |
| 2. #11763801 | C2 | semidirect |
| 3. #11763795 | C2 | semidirect |
| 4. #11763788 | C2 | semidirect |
| 6. C22×D4×C17 | C4 | semidirect |
| 12. C2×#63254 | C4 | semidirect |
| 15. C2×D4×D17 | C4 | semidirect |
| 17. C2×#63252 | C4 | semidirect |
| 19. #10587677 | C22 | semidirect |
| 20. D17⋊M16 | C22 | semidirect |
| 169. C22×D4 | #595 | semidirect |
| 178. C17 | #1795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763807 | 2 |
| #11763801 | 2 |
| #11763795 | 2 |
| #11763788 | 2 |
| C2×#10587691 | 2 |
| #1795 | 17 |