Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
320 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 21. #358×C89 | C4 | semidirect |
| 137. C89 | #13141 | semidirect |
| 150. #358 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151421 | 2 |
| C2×#19151414 | 2 |
| #26021124 | 2 |
| #26020138 | 2 |
| #26018357 | 2 |
| #26018331 | 2 |
| C89×#2141 | 2 |
| #13141 | 89 |