Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26021095 | C2 | semidirect |
| 4. #26018925 | C2 | semidirect |
| 6. C8×#13083558 | C2 | semidirect |
| 7. C89×#1567 | C2 | semidirect |
| 157. #1567 | D89 | semidirect |
| 161. C89 | #9796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151945 | 2 |
| #26021095 | 2 |
| #26021091 | 2 |
| #26018925 | 2 |
| #26018921 | 2 |
| C8×#13083558 | 2 |
| C89×#1567 | 2 |
| #9796 | 89 |