Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1190 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 203 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×#19152334 | C2 | semidirect |
| 2. C2×#19151795 | C2 | semidirect |
| 3. #26019309 | C2 | direct (N × H) |
| 4. C2×#19151342 | C2 | semidirect |
| 5. C2×#19151330 | C2 | semidirect |
| 10. #19152334 | C22 | semidirect |
| 16. #19151795 | C22 | semidirect |
| 19. #19151342 | C22 | semidirect |
| 20. #19151330 | C22 | semidirect |
| 162. C2×C89 | #1620 | semidirect |
| 171. C89 | C2×#1620 | semidirect |
| 326. C2 | #26019309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152334 | 2 |
| C2×#19151795 | 2 |
| #26019309 | 2 |
| C2×#19151342 | 2 |
| C2×#19151330 | 2 |
| C2×#493×C89 | 2 |
| C2×#1620 | 89 |