Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
346 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11763780 | C2 | semidirect |
| 2. C4×C22⋊#595 | C2 | semidirect |
| 3. #11763660 | C2 | semidirect |
| 5. C22×D4×C17 | C4 | semidirect |
| 14. #10587624 | C4 | semidirect |
| 16. C2×C4⋊Dic17 | C4 | semidirect |
| 18. (C2×#595)⋊C4 | C22 | semidirect |
| 19. #10587543 | C22 | semidirect |
| 109. C22×D4 | #595 | semidirect |
| 123. C17 | #1507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763780 | 2 |
| C4×C22⋊#595 | 2 |
| #11763660 | 2 |
| C2×#10587624 | 2 |
| #1507 | 17 |