Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1766 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1766 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×#19151391 | C2 | semidirect |
| 2. #26020167 | C2 | semidirect |
| 5. C2×#15667927 | C22 | semidirect |
| 9. C23×D4×C89 | C4 | semidirect |
| 13. C2×#127×C89 | C4 | semidirect |
| 15. C22×C42×C89 | C4 | semidirect |
| 84. C2×D4×C89 | C22⋊C4 | semidirect |
| 96. C42×C89 | C22⋊C4 | semidirect |
| 163. C22×C89 | #353 | semidirect |
| 183. C89 | #12693 | semidirect |
| 185. C23×D4 | Dic89 | semidirect |
| 189. C2×#127 | Dic89 | semidirect |
| 191. C22×C42 | Dic89 | semidirect |
| 260. C2×D4 | C22⋊Dic89 | semidirect |
| 276. C42 | C22⋊Dic89 | semidirect |
| 343. C22 | #19151391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| #26020167 | 2 |
| C22×#127×C89 | 2 |
| #12693 | 89 |