Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
836 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 292 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. #21419336 | C3 | semidirect |
| 3. #21419335 | C3 | semidirect |
| 4. #21419334 | C3 | semidirect |
| 5. #21419333 | C3 | semidirect |
| 6. C9⋊C9×C31⋊C3 | C3 | semidirect |
| 8. C31×#6895 | C3 | semidirect |
| 16. #14578887 | C32 | semidirect |
| 17. #14578886 | C32 | semidirect |
| 18. (C31⋊C9)⋊C9 | C32 | semidirect |
| 19. (C31⋊C9)⋊C9 | C32 | semidirect |
| 20. (C31⋊C9)⋊C9 | C32 | semidirect |
| 24. C31×C9⋊C9 | C32 | semidirect |
| 61. #6895 | C31⋊C3 | direct (N × H) |
| 68. C31⋊C3 | #6895 | direct (N × H) |
| 82. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 86. C31 | C3×#6895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C31⋊C3 | 3 |
| #21419336 | 3 |
| #21419335 | 3 |
| #21419334 | 3 |
| #21419333 | 3 |
| C9⋊C9×C31⋊C3 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| C31×#6895 | 3 |
| C3×#6895 | 31 |