Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1206 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×#19151393 | C2 | semidirect |
| 8. C23×Q8×C89 | C4 | semidirect |
| 12. C2×#124×C89 | C4 | semidirect |
| 15. C22×C42×C89 | C4 | semidirect |
| 64. C2×Q8×C89 | C22⋊C4 | semidirect |
| 91. C42×C89 | C22⋊C4 | semidirect |
| 146. C22×C89 | #354 | semidirect |
| 166. C89 | #12694 | semidirect |
| 167. C23×Q8 | Dic89 | semidirect |
| 171. C2×#124 | Dic89 | semidirect |
| 174. C22×C42 | Dic89 | semidirect |
| 223. C2×Q8 | C22⋊Dic89 | semidirect |
| 254. C42 | C22⋊Dic89 | semidirect |
| 309. C22 | #19151393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151393 | 2 |
| #26020167 | 2 |
| C22×#124×C89 | 2 |
| #12694 | 89 |