Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #26018751 | C2 | semidirect |
| 5. #26018154 | C2 | semidirect |
| 6. #26018110 | C2 | semidirect |
| 7. C89×#1518 | C2 | semidirect |
| 11. #19151885 | C4 | semidirect |
| 12. #19151875 | C4 | semidirect |
| 49. C4⋊#10623494 | C2×C4 | semidirect |
| 57. C4⋊Q8×C89 | C2×C4 | semidirect |
| 58. C4⋊Q8×C89 | C2×C4 | semidirect |
| 198. #1518 | D89 | semidirect |
| 203. C89 | #9175 | semidirect |
| 229. C4⋊Q8 | C4×D89 | semidirect |
| 230. C4⋊Q8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030045 | 2 |
| #26023160 | 2 |
| #26018751 | 2 |
| #26018644 | 2 |
| #26018154 | 2 |
| #26018110 | 2 |
| C89×#1518 | 2 |
| #9175 | 89 |