Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1124 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 211 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. C2×#19152039 | C2 | semidirect |
| 3. #26022186 | C2 | semidirect |
| 4. #26022169 | C2 | semidirect |
| 5. #26021972 | C2 | semidirect |
| 6. #26021863 | C2 | semidirect |
| 7. C23×Q16×C89 | C2 | semidirect |
| 11. C2×#15667958 | C22 | semidirect |
| 12. C2×#15667955 | C22 | semidirect |
| 19. #19151402 | C22 | semidirect |
| 61. C2×Q16×C89 | D4 | semidirect |
| 153. C22×C89 | #510 | semidirect |
| 170. C23×Q16 | D89 | semidirect |
| 177. C89 | #33518 | semidirect |
| 215. C2×Q16 | C22⋊D89 | semidirect |
| 325. C22 | #19152039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| #26029833 | 2 |
| #26022186 | 2 |
| #26022169 | 2 |
| #26021972 | 2 |
| #26021863 | 2 |
| C23×Q16×C89 | 2 |
| #33518 | 89 |