Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#10587498 | C2 | semidirect |
| 2. C2×#10587483 | C2 | semidirect |
| 3. #11763050 | C2 | semidirect |
| 4. #11762634 | C2 | semidirect |
| 5. #11762612 | C2 | semidirect |
| 6. #11762610 | C2 | semidirect |
| 39. #63214 | D4 | semidirect |
| 96. C17 | #2220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587498 | 2 |
| C2×#10587483 | 2 |
| #11763050 | 2 |
| #11762634 | 2 |
| #11762612 | 2 |
| #11762610 | 2 |
| C17×#466 | 2 |
| #2220 | 17 |