Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 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. #26023062 | C2 | semidirect |
| 3. #26021172 | C2 | semidirect |
| 4. #26018851 | C2 | semidirect |
| 5. #26018116 | C2 | semidirect |
| 6. #26018109 | C2 | semidirect |
| 7. C89×#1514 | C2 | semidirect |
| 9. #19151985 | C4 | semidirect |
| 10. #19151960 | C4 | semidirect |
| 58. #15667923 | C2×C4 | semidirect |
| 64. C4⋊Q8×C89 | C2×C4 | semidirect |
| 65. #127×C89 | C2×C4 | semidirect |
| 226. #1514 | D89 | semidirect |
| 229. C89 | #9381 | semidirect |
| 260. C4⋊Q8 | C4×D89 | semidirect |
| 261. #127 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031235 | 2 |
| #26023062 | 2 |
| #26021172 | 2 |
| #26018851 | 2 |
| #26018116 | 2 |
| #26018109 | 2 |
| C89×#1514 | 2 |
| #9381 | 89 |