Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26023067 | C2 | semidirect |
| 2. #26021172 | C2 | semidirect |
| 3. #26018850 | C2 | semidirect |
| 4. #26018799 | C2 | semidirect |
| 5. #26018118 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 25. #496×C89 | C4 | semidirect |
| 26. #489×C89 | C4 | semidirect |
| 60. C4⋊Q8×C89 | C2×C4 | semidirect |
| 61. #127×C89 | C2×C4 | semidirect |
| 78. #97×C89 | C2×C4 | semidirect |
| 229. C89 | #9381 | semidirect |
| 232. #496 | Dic89 | semidirect |
| 233. #489 | Dic89 | semidirect |
| 260. C4⋊Q8 | C2×Dic89 | semidirect |
| 261. #127 | C2×Dic89 | semidirect |
| 292. #97 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023067 | 2 |
| #26021172 | 2 |
| #26018850 | 2 |
| #26018799 | 2 |
| #26018118 | 2 |
| #26018107 | 2 |
| C89×#3213 | 2 |
| #9381 | 89 |