Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
568 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 12. C2×C4×#595 | C4 | semidirect |
| 15. (C2×#595)⋊C4 | C4 | semidirect |
| 16. C17×#95 | C4 | semidirect |
| 17. #10587502 | C4 | semidirect |
| 18. #10587502 | C4 | semidirect |
| 156. #95 | #595 | semidirect |
| 157. C17 | #1434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#595 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| #95×D17 | 2 |
| #1434 | 17 |