Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26033104 | C2 | semidirect |
| 2. #26022526 | C2 | semidirect |
| 3. #26022388 | C2 | semidirect |
| 4. #26022386 | C2 | semidirect |
| 5. C16×Dic178 | C2 | semidirect |
| 8. C89×#2252 | C2 | semidirect |
| 36. D1424 | Q8 | semidirect |
| 58. D712 | C2×Q8 | semidirect |
| 75. C16×C89 | C2×Q8 | semidirect |
| 90. Dic178 | D16 | semidirect |
| 114. #2252 | D89 | semidirect |
| 120. C89 | Q8×D16 | semidirect |
| 187. C16 | Q8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033104 | 2 |
| #26022526 | 2 |
| #26022388 | 2 |
| #26022386 | 2 |
| C16×Dic178 | 2 |
| C4×D1424 | 2 |
| #26022098 | 2 |
| C89×#2252 | 2 |
| Q8×D16 | 89 |