Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1008 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1008 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. #26020180 | C2 | semidirect |
| 2. #26020164 | C2 | semidirect |
| 3. #26018600 | C2 | semidirect |
| 7. #19151562 | C22 | semidirect |
| 10. C2×C22⋊#10623494 | C22 | semidirect |
| 235. C89 | #8539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020180 | 2 |
| #26020164 | 2 |
| #26018600 | 2 |
| C89×#3485 | 2 |
| #8539 | 89 |