Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
304 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q8×Dic356 | C2 | semidirect |
| 5. #26018309 | C2 | semidirect |
| 6. #26018217 | C2 | semidirect |
| 7. C89×Q8⋊C16 | C2 | semidirect |
| 60. Dic356 | SD16 | semidirect |
| 86. Q8×C89 | SD32 | semidirect |
| 133. Q8⋊C16 | D89 | semidirect |
| 135. C89 | #12354 | semidirect |
| 218. Q8 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic356 | 2 |
| #26022476 | 2 |
| #26022293 | 2 |
| #26019612 | 2 |
| #26018309 | 2 |
| #26018217 | 2 |
| C89×Q8⋊C16 | 2 |
| #12354 | 89 |