Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
524 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 10. C2×C4×Q8×C89 | C4 | semidirect |
| 12. #391×C89 | C4 | semidirect |
| 16. #384×C89 | C4 | semidirect |
| 17. #376×C89 | C4 | semidirect |
| 53. C2×Q8×C89 | C4⋊C4 | semidirect |
| 82. C42×C89 | C4⋊C4 | semidirect |
| 155. C89 | #12800 | semidirect |
| 157. C2×C4×Q8 | Dic89 | semidirect |
| 160. #391 | Dic89 | semidirect |
| 164. #384 | Dic89 | semidirect |
| 166. #376 | Dic89 | semidirect |
| 200. C2×Q8 | C4⋊Dic89 | semidirect |
| 233. C42 | C4⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151393 | 2 |
| #26020240 | 2 |
| #26018377 | 2 |
| C89×#2326 | 2 |
| #12800 | 89 |