Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1106 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1106 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 1. #26030347 | C2 | semidirect |
| 3. #26019277 | C2 | semidirect |
| 4. #26019175 | C2 | semidirect |
| 5. #26018764 | C2 | semidirect |
| 6. #26018593 | C2 | semidirect |
| 7. C89×#3501 | C2 | semidirect |
| 57. C4⋊Q8×C89 | D4 | semidirect |
| 58. C4⋊Q8×C89 | D4 | semidirect |
| 69. C4×Q8×C89 | D4 | semidirect |
| 202. #3501 | D89 | semidirect |
| 209. C89 | #18180 | semidirect |
| 242. C4⋊Q8 | C22⋊D89 | semidirect |
| 243. C4⋊Q8 | C22⋊D89 | semidirect |
| 254. C4×Q8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030347 | 2 |
| #26023531 | 2 |
| #26019277 | 2 |
| #26019175 | 2 |
| #26018764 | 2 |
| #26018593 | 2 |
| C89×#3501 | 2 |
| #18180 | 89 |