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×#14578911 | C3 | semidirect |
| 2. C32×#11719687 | C3 | semidirect |
| 3. #21419416 | C3 | direct (N × H) |
| 4. C3×#14578902 | C3 | semidirect |
| 5. C3×#14578896 | C3 | semidirect |
| 6. C3×#14578893 | C3 | semidirect |
| 7. C3×C31×#732 | C3 | semidirect |
| 10. #14578911 | C32 | semidirect |
| 15. C3×#11719687 | C32 | semidirect |
| 19. #14578902 | C32 | semidirect |
| 20. #14578896 | C32 | semidirect |
| 21. #14578893 | C32 | semidirect |
| 24. C31×#732 | C32 | semidirect |
| 67. C3×#732 | C31⋊C3 | semidirect |
| 73. C3×C31 | #6913 | semidirect |
| 90. #732 | C3×C31⋊C3 | semidirect |
| 93. C31 | C3×#6913 | semidirect |
| 135. C3 | #21419416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578911 | 3 |
| C32×#11719687 | 3 |
| #21419416 | 3 |
| C3×#14578902 | 3 |
| C3×#14578896 | 3 |
| C3×#14578893 | 3 |
| C3×C31×#732 | 3 |
| C3×#6913 | 31 |