Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
302 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 4. #19152076 | C4 | semidirect |
| 6. C2×#15667931 | C4 | semidirect |
| 10. #19151338 | C4 | semidirect |
| 14. #354×C89 | C4 | semidirect |
| 126. C89 | #7489 | semidirect |
| 134. #354 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020656 | 2 |
| C2×#19151338 | 2 |
| C2×#354×C89 | 2 |
| #7489 | 89 |