Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1046 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 1046 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#19151749 | C2 | semidirect |
| 3. #26026180 | C2 | semidirect |
| 4. C2×#19151334 | C2 | semidirect |
| 5. C2×#19151331 | C2 | semidirect |
| 6. #26018095 | C2 | semidirect |
| 7. C89×#1438 | C2 | semidirect |
| 284. #1438 | D89 | semidirect |
| 286. C89 | #9963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151749 | 2 |
| C2×#19151732 | 2 |
| #26026180 | 2 |
| C2×#19151334 | 2 |
| C2×#19151331 | 2 |
| #26018095 | 2 |
| C89×#1438 | 2 |
| #9963 | 89 |