Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26020001 | C2 | semidirect |
| 3. #26018133 | C2 | semidirect |
| 8. #19151338 | C4 | semidirect |
| 20. #15667923 | C2×C4 | semidirect |
| 140. C89 | #8224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020001 | 2 |
| C2×#19151338 | 2 |
| #26018133 | 2 |
| C4×#124×C89 | 2 |
| #8224 | 89 |