Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
210 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 27 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. #26018415 | C2 | semidirect |
| 2. #26018289 | C2 | semidirect |
| 6. D42×C89 | C4 | semidirect |
| 9. #331×C89 | C4 | semidirect |
| 92. C89 | #7515 | semidirect |
| 93. D42 | Dic89 | semidirect |
| 98. #331 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018415 | 2 |
| #26018289 | 2 |
| C89×#1619 | 2 |
| #7515 | 89 |