Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1318 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 2. #26028695 | C2 | semidirect |
| 3. #26020719 | C2 | semidirect |
| 4. #26020714 | C2 | semidirect |
| 5. #26020332 | C2 | semidirect |
| 6. #26020178 | C2 | semidirect |
| 7. C89×#1821 | C2 | semidirect |
| 190. #1821 | D89 | semidirect |
| 192. C89 | #21757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152179 | 2 |
| #26028695 | 2 |
| #26020719 | 2 |
| #26020714 | 2 |
| #26020332 | 2 |
| #26020178 | 2 |
| C89×#1821 | 2 |
| #21757 | 89 |