Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26028910 | C2 | semidirect |
| 5. #26018128 | C2 | semidirect |
| 6. #26018100 | C2 | semidirect |
| 7. C89×#1826 | C2 | semidirect |
| 16. C2×#15667945 | C4 | semidirect |
| 17. C2×#15667943 | C4 | semidirect |
| 19. C2×#15667932 | C4 | semidirect |
| 20. C2×#15667932 | C4 | semidirect |
| 226. #1826 | D89 | semidirect |
| 231. C89 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151922 | 2 |
| #26028910 | 2 |
| #26018767 | 2 |
| #26018613 | 2 |
| #26018128 | 2 |
| #26018100 | 2 |
| C89×#1826 | 2 |
| #9242 | 89 |