Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
608 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 167 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. #26033227 | C2 | semidirect |
| 2. #26022502 | C2 | semidirect |
| 3. #26022288 | C2 | semidirect |
| 4. C4×D1424 | C2 | semidirect |
| 5. Q8×C16×C89 | C2 | semidirect |
| 48. C16×C89 | #41 | semidirect |
| 50. Q8×C89 | D16 | semidirect |
| 80. Q8×C16 | D89 | semidirect |
| 82. C89 | #33958 | semidirect |
| 125. C16 | #13083575 | semidirect |
| 127. Q8 | D1424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033227 | 2 |
| #26022502 | 2 |
| #26022288 | 2 |
| C4×D1424 | 2 |
| Q8×C16×C89 | 2 |
| #33958 | 89 |