Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
300 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. C2×#19151375 | C2 | semidirect |
| 5. #26018338 | C2 | semidirect |
| 6. #26018335 | C2 | semidirect |
| 7. C89×#2153 | C2 | semidirect |
| 139. #2153 | D89 | semidirect |
| 146. C89 | #13127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021879 | 2 |
| #26021872 | 2 |
| C2×#19151375 | 2 |
| #26020098 | 2 |
| #26018338 | 2 |
| #26018335 | 2 |
| C89×#2153 | 2 |
| #13127 | 89 |