Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
382 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26022046 | C2 | semidirect |
| 3. C2×#19151415 | C2 | semidirect |
| 4. C2×#19151413 | C2 | semidirect |
| 7. C89×#1388 | C2 | semidirect |
| 165. #1388 | D89 | semidirect |
| 166. C89 | #13390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151874 | 2 |
| #26022046 | 2 |
| C2×#19151415 | 2 |
| C2×#19151413 | 2 |
| #26021879 | 2 |
| #26020299 | 2 |
| C89×#1388 | 2 |
| #13390 | 89 |