Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
560 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 64 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. #21419312 | C3 | semidirect |
| 4. #21419202 | C3 | semidirect |
| 5. C31×#6891 | C3 | semidirect |
| 11. C3×#11719689 | C32 | semidirect |
| 19. C32⋊(C31⋊C9) | C32 | semidirect |
| 21. C3×3−1+2×C31 | C32 | semidirect |
| 80. #6891 | C31⋊C3 | semidirect |
| 98. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 110. C31 | #10624590 | semidirect |
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 |
| #21419312 | 3 |
| #21419202 | 3 |
| C31×#6891 | 3 |
| #10624590 | 31 |