Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
296 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 39 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. #26018188 | C2 | semidirect |
| 2. #26018137 | C2 | semidirect |
| 6. #575×C89 | C4 | semidirect |
| 10. H(3,ℤ/4)×C89 | C4 | semidirect |
| 120. C89 | #7396 | semidirect |
| 121. #575 | Dic89 | semidirect |
| 127. H(3,ℤ/4) | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018188 | 2 |
| #26018137 | 2 |
| C89×#2010 | 2 |
| #7396 | 89 |