Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11762751 | C2 | semidirect |
| 3. #11762730 | C2 | semidirect |
| 5. #11762715 | C2 | semidirect |
| 6. #11762693 | C2 | semidirect |
| 33. C22×C4×C17 | Q8 | semidirect |
| 139. C17 | #2665 | semidirect |
| 149. C22×C4 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762751 | 2 |
| #11762732 | 2 |
| #11762730 | 2 |
| #11762721 | 2 |
| #11762715 | 2 |
| #11762693 | 2 |
| #11762672 | 2 |
| #11762669 | 2 |
| C4×C22⋊C4×C17 | 2 |
| #2665 | 17 |