Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1138 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 187 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×#19151988 | C2 | semidirect |
| 2. C2×#19151964 | C2 | semidirect |
| 3. #26019545 | C2 | direct (N × H) |
| 4. C2×#19151340 | C2 | semidirect |
| 5. C2×#19151338 | C2 | semidirect |
| 6. C2×#562×C89 | C2 | semidirect |
| 11. #19151988 | C22 | semidirect |
| 13. #19151964 | C22 | semidirect |
| 17. #19151340 | C22 | semidirect |
| 18. #19151338 | C22 | semidirect |
| 21. #562×C89 | C22 | semidirect |
| 158. C2×C89 | #1656 | semidirect |
| 162. C2×#562 | D89 | semidirect |
| 168. C89 | C2×#1656 | semidirect |
| 173. #562 | C2×D89 | semidirect |
| 320. C2 | #26019545 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151988 | 2 |
| C2×#19151964 | 2 |
| #26019545 | 2 |
| C2×#19151340 | 2 |
| C2×#19151338 | 2 |
| C2×#562×C89 | 2 |
| C2×#1656 | 89 |