Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
408 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26021937 | C2 | semidirect |
| 3. #26018411 | C2 | semidirect |
| 4. #26018408 | C2 | semidirect |
| 5. C89×#2126 | C2 | semidirect |
| 8. #19152148 | C4 | semidirect |
| 9. #19151993 | C4 | semidirect |
| 12. #19151988 | C4 | semidirect |
| 16. C2×#15667923 | C4 | semidirect |
| 175. #2126 | D89 | semidirect |
| 178. C89 | #13577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030697 | 2 |
| #26021937 | 2 |
| #26018411 | 2 |
| #26018408 | 2 |
| C89×#2126 | 2 |
| #13577 | 89 |