Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 43 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. #26018377 | C2 | semidirect |
| 2. #26018184 | C2 | semidirect |
| 7. C2×#127×C89 | C4 | semidirect |
| 10. #336×C89 | C4 | semidirect |
| 129. C89 | #7402 | semidirect |
| 131. C2×#127 | Dic89 | semidirect |
| 135. #336 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018377 | 2 |
| #26018184 | 2 |
| C89×#2011 | 2 |
| #7402 | 89 |