Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
456 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
| 2. #11762743 | C2 | semidirect |
| 3. #11762693 | C2 | semidirect |
| 4. #11762693 | C2 | semidirect |
| 139. C17 | #2569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762751 | 2 |
| #11762743 | 2 |
| #11762693 | 2 |
| #11762681 | 2 |
| #11762669 | 2 |
| #11762667 | 2 |
| C2×#10587502 | 2 |
| C4×C22⋊C4×C17 | 2 |
| #2569 | 17 |