Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1376 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1376 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×H(3,𝔽3)×C31⋊C3 | C3 | semidirect |
| 2. C32×C9×C31⋊C3 | C3 | semidirect |
| 3. C3×#14578900 | C3 | semidirect |
| 4. C3×#14578899 | C3 | semidirect |
| 5. #732×C31⋊C3 | C3 | direct (N × H) |
| 6. C3×C31×#732 | C3 | semidirect |
| 10. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 12. H(3,𝔽3)×C31⋊C3 | C32 | semidirect |
| 13. C32×C31⋊C9 | C32 | semidirect |
| 17. C3×C9×C31⋊C3 | C32 | semidirect |
| 18. #14578900 | C32 | semidirect |
| 19. #14578899 | C32 | semidirect |
| 20. C3×H(3,𝔽3)×C31 | C32 | semidirect |
| 21. C32×C9×C31 | C32 | semidirect |
| 22. C31×#732 | C32 | semidirect |
| 34. H(3,𝔽3)×C31 | C33 | semidirect |
| 37. C3×C9×C31 | C33 | semidirect |
| 40. C32⋊(C31⋊C3) | C33 | semidirect |
| 43. C3×C31⋊C9 | C33 | semidirect |
| 59. C3×C31⋊C3 | #732 | direct (N × H) |
| 69. C3×#732 | C31⋊C3 | direct (N × H) |
| 73. C3×C31 | C3×#732 | semidirect |
| 77. C31⋊C3 | C3×#732 | direct (N × H) |
| 84. C3×H(3,𝔽3) | C3×C31⋊C3 | semidirect |
| 90. C32×C9 | C3×C31⋊C3 | semidirect |
| 93. #732 | C3×C31⋊C3 | direct (N × H) |
| 94. C31 | C32×#732 | semidirect |
| 109. H(3,𝔽3) | C32×C31⋊C3 | semidirect |
| 117. C3×C9 | C32×C31⋊C3 | semidirect |
| 141. C3 | #732×C31⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C31⋊C3 | 3 |
| C32×C9×C31⋊C3 | 3 |
| C3×#14578900 | 3 |
| C3×#14578899 | 3 |
| #732×C31⋊C3 | 3 |
| C3×C31×#732 | 3 |
| C32×#732 | 31 |