Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
914 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 914 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. #26018377 | C2 | semidirect |
| 8. C22×C4⋊C4×C89 | C4 | semidirect |
| 10. C22×C42×C89 | C4 | semidirect |
| 12. #390×C89 | C4 | semidirect |
| 175. C89 | #12856 | semidirect |
| 177. C22×C4⋊C4 | Dic89 | semidirect |
| 179. C22×C42 | Dic89 | semidirect |
| 183. #390 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020167 | 2 |
| #26018377 | 2 |
| C2×#390×C89 | 2 |
| #12856 | 89 |