Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
562 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 165 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. Q8×D712 | C2 | semidirect |
| 3. #26022476 | C2 | semidirect |
| 4. #26022390 | C2 | semidirect |
| 5. #26022288 | C2 | semidirect |
| 6. C4×D1424 | C2 | semidirect |
| 7. Q8×C16×C89 | C2 | semidirect |
| 59. D712 | #41 | semidirect |
| 74. Q8×C89 | D16 | semidirect |
| 116. Q8×C16 | D89 | semidirect |
| 118. C89 | #33925 | semidirect |
| 186. Q8 | D1424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033227 | 2 |
| Q8×D712 | 2 |
| #26022476 | 2 |
| #26022390 | 2 |
| #26022288 | 2 |
| C4×D1424 | 2 |
| Q8×C16×C89 | 2 |
| #33925 | 89 |