Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 12. C4×C4⋊C4×C89 | C4 | semidirect |
| 14. #376×C89 | C4 | semidirect |
| 15. C43×C89 | C4 | semidirect |
| 100. C89 | #8740 | semidirect |
| 106. C4×C4⋊C4 | Dic89 | semidirect |
| 108. #376 | Dic89 | semidirect |
| 109. C43 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020335 | 2 |
| #26020329 | 2 |
| #26018105 | 2 |
| C89×#2298 | 2 |
| #8740 | 89 |