Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
278 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 71 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. #11762852 | C2 | semidirect |
| 4. C2×#10587507 | C2 | semidirect |
| 5. #11762716 | C2 | semidirect |
| 6. #11762568 | C2 | semidirect |
| 147. C17 | #2038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762852 | 2 |
| C2×#10587508 | 2 |
| #11762810 | 2 |
| C2×#10587507 | 2 |
| #11762716 | 2 |
| #11762568 | 2 |
| C17×#536 | 2 |
| #2038 | 17 |