Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1136 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1136 conjugacy classes of subgroups — too many to draw. Only its 155 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×#19152328 | C2 | semidirect |
| 3. #26022281 | C2 | direct (N × H) |
| 4. C2×#19151397 | C2 | semidirect |
| 5. C2×#19151396 | C2 | semidirect |
| 10. #19152328 | C22 | semidirect |
| 20. #19151397 | C22 | semidirect |
| 21. #19151396 | C22 | semidirect |
| 216. C2×C89 | #2205 | semidirect |
| 224. C89 | C2×#2205 | semidirect |
| 433. C2 | #26022281 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152328 | 2 |
| C2×#19151781 | 2 |
| #26022281 | 2 |
| C2×#19151397 | 2 |
| C2×#19151396 | 2 |
| C2×#456×C89 | 2 |
| C2×#2205 | 89 |