Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
764 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 202 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. C22×#63247 | C2 | semidirect |
| 2. #11763782 | C2 | semidirect |
| 3. #11763781 | C2 | semidirect |
| 4. #11763779 | C2 | semidirect |
| 18. C2×#63247 | C22 | semidirect |
| 19. C22×#3624 | C22 | semidirect |
| 20. C22⋊#3624 | C22 | semidirect |
| 21. #10587543 | C22 | semidirect |
| 129. C17 | #2879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63247 | 2 |
| #11763782 | 2 |
| #11763781 | 2 |
| #11763779 | 2 |
| C22×#63254 | 2 |
| #2879 | 17 |