Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1232 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 328 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. C32×#11719689 | C3 | semidirect |
| 3. C33×C31⋊C9 | C3 | semidirect |
| 4. #21419323 | C3 | direct (N × H) |
| 5. C3×(C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 6. C32×3−1+2×C31 | C3 | semidirect |
| 9. C3×#11719689 | C32 | semidirect |
| 15. C32×C31⋊C9 | C32 | semidirect |
| 16. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 19. C3×3−1+2×C31 | C32 | semidirect |
| 52. C32×3−1+2 | C31⋊C3 | semidirect |
| 58. C3×C31 | #6893 | semidirect |
| 67. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 76. C31 | C3×#6893 | semidirect |
| 108. C3 | #21419323 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719689 | 3 |
| C32×C32⋊(C31⋊C3) | 3 |
| C33×C31⋊C9 | 3 |
| #21419323 | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C32×3−1+2×C31 | 3 |
| C3×#6893 | 31 |