Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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. #11763781 | C2 | semidirect |
| 2. #11763752 | C2 | semidirect |
| 3. #11763660 | C2 | semidirect |
| 5. C22×D4×C17 | C4 | semidirect |
| 13. #10587624 | C4 | semidirect |
| 15. C2×C4⋊Dic17 | C4 | semidirect |
| 17. (C2×#595)⋊C4 | C22 | semidirect |
| 19. #10587543 | C22 | semidirect |
| 108. C22×D4 | #595 | semidirect |
| 122. C17 | #1510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763781 | 2 |
| #11763752 | 2 |
| #11763660 | 2 |
| C2×#10587624 | 2 |
| #1510 | 17 |