Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1200 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 171 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×#19151780 | C2 | semidirect |
| 2. C2×#19151770 | C2 | semidirect |
| 3. #26022278 | C2 | direct (N × H) |
| 4. C2×#19151397 | C2 | semidirect |
| 5. C2×#19151395 | C2 | semidirect |
| 6. C2×#555×C89 | C2 | semidirect |
| 11. #19151780 | C22 | semidirect |
| 13. #19151770 | C22 | semidirect |
| 18. #19151397 | C22 | semidirect |
| 19. #19151395 | C22 | semidirect |
| 22. #555×C89 | C22 | semidirect |
| 224. C2×C89 | #2204 | semidirect |
| 227. C2×#555 | D89 | semidirect |
| 233. C89 | C2×#2204 | semidirect |
| 239. #555 | C2×D89 | semidirect |
| 451. C2 | #26022278 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151780 | 2 |
| C2×#19151770 | 2 |
| #26022278 | 2 |
| C2×#19151397 | 2 |
| C2×#19151395 | 2 |
| C2×#555×C89 | 2 |
| C2×#2204 | 89 |