Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
684 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26020176 | C2 | semidirect |
| 4. #26018158 | C2 | semidirect |
| 108. C23×C89 | #101 | semidirect |
| 177. C89 | #9505 | semidirect |
| 280. C23 | #15667931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029281 | 2 |
| #26020176 | 2 |
| #26018590 | 2 |
| #26018158 | 2 |
| C89×#2409 | 2 |
| #9505 | 89 |