Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
4122 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 4122 conjugacy classes of subgroups — too many to draw. Only its 555 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. C22×#15667927 | C2 | semidirect |
| 2. #26022830 | C2 | semidirect |
| 3. #26020200 | C2 | semidirect |
| 5. C22×C22⋊Dic89 | C22 | semidirect |
| 6. C22×C22⋊Dic89 | C22 | semidirect |
| 8. C2×#15667927 | C22 | semidirect |
| 10. #19151478 | C22 | semidirect |
| 15. C2×H(5,𝔽2)×C89 | C4 | semidirect |
| 21. C23×Dic89 | C23 | semidirect |
| 27. C2×C22⋊Dic89 | C23 | semidirect |
| 36. H(5,𝔽2)×C89 | C2×C4 | semidirect |
| 74. C24×C89 | C22⋊C4 | semidirect |
| 99. C2×D4×C89 | C22⋊C4 | semidirect |
| 107. C22×C4×C89 | C22⋊C4 | semidirect |
| 188. C89 | #20609 | semidirect |
| 191. C2×H(5,𝔽2) | Dic89 | semidirect |
| 210. H(5,𝔽2) | C2×Dic89 | semidirect |
| 248. C24 | C22⋊Dic89 | semidirect |
| 273. C2×D4 | C22⋊Dic89 | semidirect |
| 286. C22×C4 | C22⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667927 | 2 |
| #26022830 | 2 |
| #26020200 | 2 |
| C22×H(5,𝔽2)×C89 | 2 |
| #20609 | 89 |