Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1342 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 239 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. #493×D89 | C2 | semidirect |
| 2. #26019867 | C2 | semidirect |
| 3. #26019866 | C2 | semidirect |
| 4. C82×D89 | C2 | semidirect |
| 5. C89×#1712 | C2 | semidirect |
| 8. #19151975 | C22 | semidirect |
| 9. #19151974 | C22 | semidirect |
| 12. C8×#10623494 | C22 | semidirect |
| 13. #493×C89 | C22 | semidirect |
| 14. C82×C89 | C22 | semidirect |
| 36. C8×D89 | D8 | semidirect |
| 52. C8×C89 | C2×D8 | semidirect |
| 53. #10623494 | C2×D8 | semidirect |
| 65. D89 | #1712 | direct (N × H) |
| 69. #1712 | D89 | direct (N × H) |
| 71. C89 | C2×#1712 | semidirect |
| 77. #493 | C2×D89 | semidirect |
| 80. C82 | C2×D89 | semidirect |
| 119. C8 | D8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D89 | 2 |
| #26019867 | 2 |
| #26019866 | 2 |
| C82×D89 | 2 |
| C89×#1712 | 2 |
| C2×#1712 | 89 |