Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1252 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. #26034657 | C2 | semidirect |
| 2. #26030702 | C2 | semidirect |
| 3. #26019540 | C2 | semidirect |
| 4. #26018844 | C2 | semidirect |
| 5. #26018843 | C2 | semidirect |
| 6. C89×#3151 | C2 | semidirect |
| 8. #19152340 | C22 | semidirect |
| 16. #19151985 | C22 | semidirect |
| 19. C4×#13083558 | C22 | semidirect |
| 20. #19151338 | C22 | semidirect |
| 21. #19151337 | C22 | semidirect |
| 24. C2×#127×C89 | C22 | semidirect |
| 25. #496×C89 | C22 | semidirect |
| 28. C4×M16×C89 | C22 | semidirect |
| 183. #3151 | D89 | semidirect |
| 187. C89 | #19073 | semidirect |
| 199. C2×#127 | C2×D89 | semidirect |
| 201. #496 | C2×D89 | semidirect |
| 207. C4×M16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034657 | 2 |
| #26030702 | 2 |
| #26019540 | 2 |
| #26018844 | 2 |
| #26018843 | 2 |
| C89×#3151 | 2 |
| #19073 | 89 |