Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1072 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1072 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 |
|---|---|---|
| 2. #26030648 | C2 | semidirect |
| 3. #26019556 | C2 | semidirect |
| 4. #26018844 | C2 | semidirect |
| 5. #26018843 | C2 | semidirect |
| 6. C89×#3152 | C2 | semidirect |
| 15. #19151960 | C22 | semidirect |
| 19. C4×#13083558 | C22 | semidirect |
| 20. #19151338 | C22 | semidirect |
| 21. #19151337 | C22 | semidirect |
| 24. C2×C4⋊Q8×C89 | C22 | semidirect |
| 25. #497×C89 | C22 | semidirect |
| 28. C4×M16×C89 | C22 | semidirect |
| 172. #3152 | D89 | semidirect |
| 177. C89 | #19074 | semidirect |
| 188. C2×C4⋊Q8 | C2×D89 | semidirect |
| 189. #497 | C2×D89 | semidirect |
| 197. 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 |
| #26030648 | 2 |
| #26019556 | 2 |
| #26018844 | 2 |
| #26018843 | 2 |
| C89×#3152 | 2 |
| #19074 | 89 |