Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11763810 | C2 | semidirect |
| 2. C2×#10587549 | C2 | semidirect |
| 4. C4×C4⋊#595 | C2 | semidirect |
| 11. C17×#124 | C4 | semidirect |
| 12. #10587633 | C4 | semidirect |
| 13. #10587622 | C4 | semidirect |
| 18. #10587561 | C4 | semidirect |
| 136. #124 | #595 | semidirect |
| 147. C17 | #1983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763810 | 2 |
| C2×#10587549 | 2 |
| C2×#10587547 | 2 |
| C4×C4⋊#595 | 2 |
| #124×D17 | 2 |
| #1983 | 17 |