Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
5502 conjugacy classes of subgroups; only the 3307 normal subgroups are shown.
This group has 5502 conjugacy classes of subgroups — too many to draw. Only its 3307 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×#19151468 | C2 | direct (N × H) |
| 7. #19151468 | C22 | direct (N × H) |
| 9. C22×C42×C89 | C4 | semidirect |
| 20. C2×C42×C89 | C2×C4 | semidirect |
| 30. C22×C4×C89 | C4⋊C4 | semidirect |
| 35. C42×C89 | C22×C4 | semidirect |
| 43. C2×C4×C89 | C2×C4⋊C4 | semidirect |
| 49. C22×C89 | #384 | semidirect |
| 56. C4×C89 | C22×C4⋊C4 | semidirect |
| 59. C2×C89 | C2×#384 | semidirect |
| 66. C89 | C22×#384 | semidirect |
| 71. C22×C42 | Dic89 | semidirect |
| 83. C2×C42 | C2×Dic89 | semidirect |
| 92. C22×C4 | C4⋊Dic89 | semidirect |
| 98. C42 | C22×Dic89 | semidirect |
| 108. C2×C4 | C2×C4⋊Dic89 | semidirect |
| 112. C22 | #19151468 | direct (N × H) |
| 120. C4 | C22×C4⋊Dic89 | semidirect |
| 121. C2 | C2×#19151468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Dic89 | 2 |
| C2×#19151468 | 2 |
| C23×C42×C89 | 2 |
| C22×#384 | 89 |