Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1088 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1088 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 |
|---|---|---|
| 1. C32×#11719689 | C3 | semidirect |
| 2. C32×#11719689 | C3 | semidirect |
| 4. #21419402 | C3 | direct (N × H) |
| 5. C3×#14578898 | C3 | semidirect |
| 6. C32×3−1+2×C31 | C3 | semidirect |
| 15. C3×#11719689 | C32 | semidirect |
| 16. C3×#11719689 | C32 | semidirect |
| 17. C3×#11719689 | C32 | semidirect |
| 24. C32×C31⋊C9 | C32 | semidirect |
| 25. #14578898 | C32 | semidirect |
| 30. C3×3−1+2×C31 | C32 | semidirect |
| 31. C3×3−1+2×C31 | C32 | semidirect |
| 46. 3−1+2×C31 | C33 | semidirect |
| 59. #11719689 | C33 | semidirect |
| 64. C3×C31⋊C9 | C33 | semidirect |
| 86. C32×3−1+2 | C31⋊C3 | semidirect |
| 95. C3×C31 | #6910 | semidirect |
| 113. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 114. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 124. C31 | C3×#6910 | semidirect |
| 145. 3−1+2 | C32×C31⋊C3 | semidirect |
| 181. C3 | #21419402 | 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 |
| #21419402 | 3 |
| C3×#14578898 | 3 |
| C32×3−1+2×C31 | 3 |
| C3×#6910 | 31 |