Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
716 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 115 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. C4×#15667931 | C2 | semidirect |
| 3. #26018838 | C2 | semidirect |
| 4. #26018663 | C2 | semidirect |
| 5. C89×#1985 | C2 | semidirect |
| 224. #1985 | D89 | semidirect |
| 228. C89 | #8402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033685 | 2 |
| C4×#15667931 | 2 |
| #26018838 | 2 |
| #26018663 | 2 |
| C89×#1985 | 2 |
| #8402 | 89 |