Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
960 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 960 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. #26021069 | C2 | semidirect |
| 2. C2×#19151338 | C2 | semidirect |
| 6. C2×#15667923 | C22 | semidirect |
| 7. #19151468 | C22 | semidirect |
| 10. H(3,𝔽4)×C89 | C4 | semidirect |
| 107. C89 | #8506 | semidirect |
| 109. H(3,𝔽4) | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021069 | 2 |
| C2×#19151338 | 2 |
| C2×H(3,𝔽4)×C89 | 2 |
| #8506 | 89 |