Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 159 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. D8×Dic178 | C2 | semidirect |
| 2. #26022527 | C2 | semidirect |
| 3. #26022526 | C2 | semidirect |
| 4. #26022389 | C2 | semidirect |
| 5. #26022387 | C2 | semidirect |
| 6. C16×Dic178 | C2 | semidirect |
| 45. D16×C89 | Q8 | semidirect |
| 68. D8×C89 | C2×Q8 | semidirect |
| 75. C16×C89 | C2×Q8 | semidirect |
| 90. Dic178 | D16 | direct (N × H) |
| 120. C89 | Q8×D16 | semidirect |
| 149. D16 | Dic178 | direct (N × H) |
| 171. D8 | C2×Dic178 | semidirect |
| 187. C16 | C2×Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic178 | 2 |
| #26022527 | 2 |
| #26022526 | 2 |
| #26022389 | 2 |
| #26022387 | 2 |
| C16×Dic178 | 2 |
| D16×Dic89 | 2 |
| C4×D16×C89 | 2 |
| Q8×D16 | 89 |