Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
502 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 2. C2×#19151431 | C2 | direct (N × H) |
| 3. C22×#15667918 | C2 | semidirect |
| 4. C22×C32×C89 | C2 | semidirect |
| 9. #19151431 | C22 | direct (N × H) |
| 10. C2×#15667918 | C22 | semidirect |
| 12. C2×C32×C89 | C22 | semidirect |
| 20. #15667918 | C23 | semidirect |
| 24. C32×C89 | C23 | semidirect |
| 49. C22×C89 | M64 | semidirect |
| 57. C2×C89 | C2×M64 | semidirect |
| 63. C22×C32 | D89 | semidirect |
| 64. C89 | C22×M64 | semidirect |
| 72. C2×C32 | C2×D89 | semidirect |
| 84. C32 | C22×D89 | semidirect |
| 111. C22 | #19151431 | direct (N × H) |
| 117. C2 | C2×#19151431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D89 | 2 |
| C2×#19151431 | 2 |
| C22×#15667918 | 2 |
| C22×C32×C89 | 2 |
| C22×M64 | 89 |