Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
990 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. C2×#19151392 | C2 | semidirect |
| 5. C23×Dic178 | C4 | semidirect |
| 7. C2×#15668010 | C4 | semidirect |
| 13. C2×#15667971 | C4 | semidirect |
| 199. C89 | #12698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152169 | 2 |
| C2×#19151392 | 2 |
| #26020170 | 2 |
| C89×#1782 | 2 |
| #12698 | 89 |