Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
368 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #26019008 | C2 | semidirect |
| 3. #26018220 | C2 | semidirect |
| 4. C4×M32×C89 | C2 | semidirect |
| 122. C4×M32 | D89 | semidirect |
| 125. C89 | #11680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030831 | 2 |
| #26019008 | 2 |
| #26018220 | 2 |
| C4×M32×C89 | 2 |
| #11680 | 89 |