Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 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 |
|---|---|---|
| 2. #26023362 | C2 | semidirect |
| 3. #26018875 | C2 | semidirect |
| 4. #26018760 | C2 | semidirect |
| 5. #26018145 | C2 | semidirect |
| 6. #26018144 | C2 | semidirect |
| 7. C89×#1505 | C2 | semidirect |
| 11. #19151990 | C4 | semidirect |
| 12. #19151985 | C4 | semidirect |
| 58. #15667923 | C2×C4 | semidirect |
| 66. C4⋊Q8×C89 | C2×C4 | semidirect |
| 67. #127×C89 | C2×C4 | semidirect |
| 231. #1505 | D89 | semidirect |
| 234. C89 | #9441 | semidirect |
| 271. C4⋊Q8 | C4×D89 | semidirect |
| 272. #127 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030720 | 2 |
| #26023362 | 2 |
| #26018875 | 2 |
| #26018760 | 2 |
| #26018145 | 2 |
| #26018144 | 2 |
| C89×#1505 | 2 |
| #9441 | 89 |