Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 56. C4⋊Q8×C89 | Q8 | semidirect |
| 188. C89 | #10359 | semidirect |
| 216. C4⋊Q8 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028524 | 2 |
| #26021226 | 2 |
| #26021073 | 2 |
| #26018134 | 2 |
| #26018133 | 2 |
| C89×#1993 | 2 |
| #10359 | 89 |