Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022163 | C2 | semidirect |
| 2. #26021250 | C2 | semidirect |
| 3. #26018261 | C2 | semidirect |
| 4. #26018176 | C2 | semidirect |
| 5. C89×#3186 | C2 | semidirect |
| 6. C22×D712 | C22 | semidirect |
| 11. C22⋊#13083549 | C22 | semidirect |
| 12. #19151361 | C22 | semidirect |
| 34. C2×D8×C89 | D4 | semidirect |
| 44. #107×C89 | D4 | semidirect |
| 100. C23×C89 | D16 | semidirect |
| 172. #3186 | D89 | semidirect |
| 177. C89 | #12102 | semidirect |
| 199. C2×D8 | C22⋊D89 | semidirect |
| 215. #107 | C22⋊D89 | semidirect |
| 279. C23 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022163 | 2 |
| #26021250 | 2 |
| #26018261 | 2 |
| #26018176 | 2 |
| C89×#3186 | 2 |
| #12102 | 89 |