Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1556 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1556 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19151385 | C2 | semidirect |
| 3. #26020661 | C2 | semidirect |
| 4. #26020651 | C2 | semidirect |
| 6. #19152073 | C22 | semidirect |
| 8. C2×#15667929 | C22 | semidirect |
| 9. C2×#15667927 | C22 | semidirect |
| 18. D42×C89 | C4 | semidirect |
| 86. C24×C89 | C22⋊C4 | semidirect |
| 105. C2×D4×C89 | C22⋊C4 | semidirect |
| 119. C22⋊C4×C89 | C22⋊C4 | semidirect |
| 121. C42×C89 | C22⋊C4 | semidirect |
| 216. C89 | #12759 | semidirect |
| 220. D42 | Dic89 | semidirect |
| 285. C24 | C22⋊Dic89 | semidirect |
| 304. C2×D4 | C22⋊Dic89 | semidirect |
| 329. C22⋊C4 | C22⋊Dic89 | semidirect |
| 332. C42 | C22⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| C2×#19151385 | 2 |
| #26020661 | 2 |
| #26020651 | 2 |
| C2×D42×C89 | 2 |
| #12759 | 89 |