Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
146 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 25 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. #26018421 | C2 | semidirect |
| 3. C89×#1411 | C2 | semidirect |
| 64. #1411 | D89 | semidirect |
| 65. C89 | #7531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019859 | 2 |
| #26018421 | 2 |
| C89×#1411 | 2 |
| #7531 | 89 |