Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 2. #11763758 | C2 | semidirect |
| 3. #11763755 | C2 | semidirect |
| 4. #11763753 | C2 | semidirect |
| 6. C4×C4⋊#595 | C2 | semidirect |
| 14. C17×#117 | C4 | semidirect |
| 15. #10587612 | C4 | semidirect |
| 16. #10587578 | C4 | semidirect |
| 19. #10587563 | C4 | semidirect |
| 20. #10587558 | C4 | semidirect |
| 21. #10587558 | C4 | semidirect |
| 135. #117 | #595 | semidirect |
| 148. C17 | #2314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763759 | 2 |
| #11763758 | 2 |
| #11763755 | 2 |
| #11763753 | 2 |
| #11763751 | 2 |
| C4×C4⋊#595 | 2 |
| #117×D17 | 2 |
| #2314 | 17 |