Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
118 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 34. Q8×C89 | C32 | semidirect |
| 59. C89 | Q8⋊C32 | semidirect |
| 90. Q8 | #15667918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊#15667918 | 2 |
| C4×#15667918 | 2 |
| Q8×C16×C89 | 2 |
| Q8⋊C32 | 89 |