Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
992 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 274 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×#14578913 | C3 | semidirect |
| 2. C3×#14578911 | C3 | semidirect |
| 3. C32×#11719689 | C3 | semidirect |
| 4. #21419412 | C3 | direct (N × H) |
| 5. C3×#14578901 | C3 | semidirect |
| 6. C3×#14578899 | C3 | semidirect |
| 7. C3×#14578898 | C3 | semidirect |
| 8. C3×#14578896 | C3 | semidirect |
| 9. C3×#14578894 | C3 | semidirect |
| 10. C3×C31×AΣL(1,𝔽27) | C3 | semidirect |
| 12. #14578913 | C32 | semidirect |
| 14. #14578911 | C32 | semidirect |
| 21. C3×#11719689 | C32 | semidirect |
| 30. #14578901 | C32 | semidirect |
| 31. #14578899 | C32 | semidirect |
| 32. #14578898 | C32 | semidirect |
| 33. #14578896 | C32 | semidirect |
| 34. #14578894 | C32 | semidirect |
| 38. C31×AΣL(1,𝔽27) | C32 | semidirect |
| 105. C3×AΣL(1,𝔽27) | C31⋊C3 | semidirect |
| 110. C3×C31 | #6913 | semidirect |
| 140. AΣL(1,𝔽27) | C3×C31⋊C3 | semidirect |
| 141. C31 | C3×#6913 | semidirect |
| 203. C3 | #21419412 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578913 | 3 |
| C3×#14578911 | 3 |
| C32×#11719689 | 3 |
| #21419412 | 3 |
| C3×#14578901 | 3 |
| C3×#14578899 | 3 |
| C3×#14578898 | 3 |
| C3×#14578896 | 3 |
| C3×#14578894 | 3 |
| C3×C31×AΣL(1,𝔽27) | 3 |
| C3×#6913 | 31 |