Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
992 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 992 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. C3×#14578912 | C3 | semidirect |
| 2. #21419419 | C3 | direct (N × H) |
| 3. C3×#14578902 | C3 | semidirect |
| 4. C3×#14578900 | C3 | semidirect |
| 5. C3×#14578897 | C3 | semidirect |
| 6. C3×#14578894 | C3 | semidirect |
| 7. C32×3−1+2×C31 | C3 | semidirect |
| 9. #14578912 | C32 | semidirect |
| 15. #14578902 | C32 | semidirect |
| 16. #14578900 | C32 | semidirect |
| 17. #14578897 | C32 | semidirect |
| 18. #14578894 | C32 | semidirect |
| 22. C3×3−1+2×C31 | C32 | semidirect |
| 66. C32×3−1+2 | C31⋊C3 | semidirect |
| 75. C3×C31 | #6913 | semidirect |
| 86. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 96. C31 | C3×#6913 | semidirect |
| 139. C3 | #21419419 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578912 | 3 |
| #21419419 | 3 |
| C3×#14578902 | 3 |
| C3×#14578900 | 3 |
| C3×#14578897 | 3 |
| C3×#14578894 | 3 |
| C32×3−1+2×C31 | 3 |
| C3×#6913 | 31 |