Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26033354 | C2 | semidirect |
| 3. #26021989 | C2 | semidirect |
| 4. #26021987 | C2 | semidirect |
| 5. #26020295 | C2 | semidirect |
| 6. #26018359 | C2 | semidirect |
| 7. C89×#1386 | C2 | semidirect |
| 15. #19151857 | C4 | semidirect |
| 16. #19151852 | C4 | semidirect |
| 50. #15667952 | D4 | semidirect |
| 63. M32×C89 | D4 | semidirect |
| 188. #1386 | D89 | semidirect |
| 189. C89 | #13077 | semidirect |
| 238. M32 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26029915 | 2 |
| #26021989 | 2 |
| #26021987 | 2 |
| #26020295 | 2 |
| #26018359 | 2 |
| C89×#1386 | 2 |
| #13077 | 89 |