Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
888 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26021081 | C2 | semidirect |
| 2. #26018987 | C2 | semidirect |
| 4. #19151622 | C22 | semidirect |
| 6. C42×Dic89 | C22 | semidirect |
| 9. H(3,𝔽4)×C89 | C4 | semidirect |
| 90. C89 | #8530 | semidirect |
| 91. H(3,𝔽4) | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021081 | 2 |
| #26018987 | 2 |
| C89×#3549 | 2 |
| #8530 | 89 |