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. #26021988 | C2 | semidirect |
| 4. #26020295 | C2 | semidirect |
| 5. #26018358 | C2 | semidirect |
| 6. #26018357 | C2 | semidirect |
| 7. C89×#2145 | C2 | semidirect |
| 14. #19151853 | C4 | semidirect |
| 15. #19151848 | C4 | semidirect |
| 43. #15667952 | D4 | semidirect |
| 65. M32×C89 | D4 | semidirect |
| 185. #2145 | D89 | semidirect |
| 189. C89 | #13077 | semidirect |
| 238. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26029910 | 2 |
| #26021988 | 2 |
| #26020295 | 2 |
| #26018358 | 2 |
| #26018357 | 2 |
| C89×#2145 | 2 |
| #13077 | 89 |