Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#19151391 | C2 | semidirect |
| 2. #26020240 | C2 | semidirect |
| 3. C4×#15667927 | C2 | semidirect |
| 12. C2×#127×C89 | C4 | semidirect |
| 19. #390×C89 | C4 | semidirect |
| 20. C4×C4⋊C4×C89 | C4 | semidirect |
| 27. #15667927 | D4 | semidirect |
| 190. C4×C89 | #353 | semidirect |
| 207. C89 | #13223 | semidirect |
| 208. C2×#127 | Dic89 | semidirect |
| 217. #390 | Dic89 | semidirect |
| 219. C4×C4⋊C4 | Dic89 | semidirect |
| 395. C4 | #19151391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| #26020240 | 2 |
| C4×#15667927 | 2 |
| C89×#2541 | 2 |
| #13223 | 89 |