Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
490 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #26018764 | C2 | semidirect |
| 5. #26018145 | C2 | semidirect |
| 6. #26018144 | C2 | semidirect |
| 7. C89×#1506 | C2 | semidirect |
| 9. #19151960 | C4 | semidirect |
| 10. #19151960 | C4 | semidirect |
| 54. #15667923 | C2×C4 | semidirect |
| 61. C4⋊Q8×C89 | C2×C4 | semidirect |
| 62. C4⋊Q8×C89 | C2×C4 | semidirect |
| 208. #1506 | D89 | semidirect |
| 211. C89 | #9439 | semidirect |
| 239. C4⋊Q8 | C4×D89 | semidirect |
| 240. C4⋊Q8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030641 | 2 |
| #26023362 | 2 |
| #26018875 | 2 |
| #26018764 | 2 |
| #26018145 | 2 |
| #26018144 | 2 |
| C89×#1506 | 2 |
| #9439 | 89 |