Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
2636 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 2636 conjugacy classes of subgroups — too many to draw. Only its 355 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. C3×3−1+2×C31⋊C3 | C3 | semidirect |
| 3. #21419312 | C3 | semidirect |
| 4. #21419311 | C3 | semidirect |
| 5. #21419310 | C3 | semidirect |
| 6. #21419309 | C3 | semidirect |
| 7. C32⋊C9×C31⋊C3 | C3 | semidirect |
| 8. C31×#6891 | C3 | semidirect |
| 16. C3×#11719689 | C32 | semidirect |
| 17. C3×#11719686 | C32 | semidirect |
| 18. C3×#11719687 | C32 | semidirect |
| 20. C3×C9×C31⋊C3 | C32 | semidirect |
| 21. C32⋊(C31⋊C9) | C32 | semidirect |
| 22. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 24. C3×3−1+2×C31 | C32 | semidirect |
| 25. C31×C32⋊C9 | C32 | semidirect |
| 43. C32×C31⋊C3 | 3−1+2 | semidirect |
| 49. C3×C9×C31 | C33 | semidirect |
| 51. C3×C31⋊C9 | C33 | semidirect |
| 61. C32×C31 | C3×3−1+2 | semidirect |
| 77. C3×C31⋊C3 | C3×3−1+2 | semidirect |
| 86. #6891 | C31⋊C3 | direct (N × H) |
| 95. C31⋊C3 | #6891 | direct (N × H) |
| 108. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 112. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 113. C31 | C3×#6891 | semidirect |
| 142. C3×C9 | C32×C31⋊C3 | semidirect |
| 163. C32 | 3−1+2×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C31⋊C3 | 3 |
| C3×3−1+2×C31⋊C3 | 3 |
| #21419312 | 3 |
| #21419311 | 3 |
| #21419310 | 3 |
| #21419309 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| C31×#6891 | 3 |
| C3×#6891 | 31 |