Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
712 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19151889 | C2 | semidirect |
| 3. #26021053 | C2 | semidirect |
| 4. C2×#19151325 | C2 | semidirect |
| 5. C89×#1296 | C2 | semidirect |
| 27. #15668012 | D4 | semidirect |
| 48. C4⋊C8×C89 | D4 | semidirect |
| 163. #1296 | D89 | semidirect |
| 164. C89 | #10235 | semidirect |
| 203. C4⋊C8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151889 | 2 |
| #26025168 | 2 |
| #26021053 | 2 |
| C2×#19151325 | 2 |
| C89×#1296 | 2 |
| #10235 | 89 |