Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 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. #26021085 | C2 | semidirect |
| 3. #26018975 | C2 | semidirect |
| 4. #26018761 | C2 | semidirect |
| 5. C89×#1536 | C2 | semidirect |
| 7. #19152314 | C4 | semidirect |
| 10. #19152233 | C4 | semidirect |
| 14. #19151622 | C22 | semidirect |
| 16. #19151444 | C22 | semidirect |
| 21. #432×C89 | C22 | semidirect |
| 158. #1536 | D89 | semidirect |
| 160. C89 | #8491 | semidirect |
| 170. #432 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034657 | 2 |
| #26021085 | 2 |
| #26018975 | 2 |
| #26018761 | 2 |
| C89×#1536 | 2 |
| #8491 | 89 |