Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 542 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. C22×D1424 | C2 | semidirect |
| 2. C2×#19151433 | C2 | direct (N × H) |
| 3. C22×#15667918 | C2 | semidirect |
| 4. C22×D16×C89 | C2 | semidirect |
| 7. C2×D1424 | C22 | semidirect |
| 8. #19151433 | C22 | direct (N × H) |
| 9. C2×#15667918 | C22 | semidirect |
| 12. C2×D16×C89 | C22 | semidirect |
| 18. D1424 | C23 | semidirect |
| 19. #15667918 | C23 | semidirect |
| 25. D16×C89 | C23 | semidirect |
| 58. C22×C89 | D32 | semidirect |
| 66. C2×C89 | C2×D32 | semidirect |
| 70. C22×D16 | D89 | semidirect |
| 73. C89 | C22×D32 | semidirect |
| 79. C2×D16 | C2×D89 | semidirect |
| 93. D16 | C22×D89 | semidirect |
| 129. C22 | #19151433 | direct (N × H) |
| 135. C2 | C2×#19151433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| C2×#19151433 | 2 |
| C22×#15667918 | 2 |
| C22×D16×C89 | 2 |
| C22×D32 | 89 |