Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 552 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. #26033258 | C2 | semidirect |
| 3. #26022508 | C2 | semidirect |
| 4. #26022298 | C2 | semidirect |
| 5. #26022293 | C2 | semidirect |
| 6. C4×#15667957 | C2 | semidirect |
| 7. Q8×C16×C89 | C2 | semidirect |
| 72. C16×C89 | #41 | semidirect |
| 74. Q8×C89 | SD32 | semidirect |
| 112. Q8×C16 | D89 | semidirect |
| 114. C89 | #33959 | semidirect |
| 179. C16 | #13083575 | semidirect |
| 183. Q8 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033258 | 2 |
| #26033227 | 2 |
| #26022508 | 2 |
| #26022298 | 2 |
| #26022293 | 2 |
| C4×#15667957 | 2 |
| Q8×C16×C89 | 2 |
| #33959 | 89 |