Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
712 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 199. Dic178 | #101 | semidirect |
| 236. C89 | #8374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152325 | 2 |
| C4×#15667930 | 2 |
| #26018854 | 2 |
| #26018700 | 2 |
| #26018698 | 2 |
| #26018595 | 2 |
| C89×#1528 | 2 |
| #8374 | 89 |