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×#11719687 | C3 | semidirect |
| 4. #21419417 | C3 | direct (N × H) |
| 5. C3×#14578901 | C3 | semidirect |
| 6. C3×#14578899 | C3 | semidirect |
| 7. C3×#14578897 | C3 | semidirect |
| 8. C3×#14578895 | C3 | semidirect |
| 9. C3×#14578893 | C3 | semidirect |
| 10. C3×C31×#731 | C3 | semidirect |
| 13. #14578913 | C32 | semidirect |
| 15. #14578911 | C32 | semidirect |
| 24. C3×#11719687 | C32 | semidirect |
| 30. #14578901 | C32 | semidirect |
| 31. #14578899 | C32 | semidirect |
| 32. #14578897 | C32 | semidirect |
| 33. #14578895 | C32 | semidirect |
| 34. #14578893 | C32 | semidirect |
| 38. C31×#731 | C32 | semidirect |
| 103. C3×#731 | C31⋊C3 | semidirect |
| 109. C3×C31 | #6913 | semidirect |
| 138. #731 | C3×C31⋊C3 | semidirect |
| 141. C31 | C3×#6913 | semidirect |
| 203. C3 | #21419417 | 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×#11719687 | 3 |
| #21419417 | 3 |
| C3×#14578901 | 3 |
| C3×#14578899 | 3 |
| C3×#14578897 | 3 |
| C3×#14578895 | 3 |
| C3×#14578893 | 3 |
| C3×C31×#731 | 3 |
| C3×#6913 | 31 |