Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 498 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. #26018968 | C2 | semidirect |
| 4. #26018109 | C2 | semidirect |
| 163. C89 | #9453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025425 | 2 |
| #26018968 | 2 |
| #26018593 | 2 |
| #26018109 | 2 |
| C89×#2973 | 2 |
| #9453 | 89 |