Finite Group DatabasebetaFinite Group Databasebeta← C31⋊C3×C32⋊H(3,𝔽3) #36382280
Order 22599.
3824 conjugacy classes of subgroups.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C34×C31⋊C3 | C3 | semidirect |
| 2. C3×H(3,𝔽3)×C31⋊C3 | C3 | semidirect |
| 3. #21419308 | C3 | semidirect |
| 4. (C3×C31⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 5. C31×C32⋊H(3,𝔽3) | C3 | semidirect |
| 8. C33×C31⋊C3 | C32 | semidirect |
| 9. C33×C31⋊C3 | C32 | semidirect |
| 10. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 11. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 13. C34×C31 | C32 | semidirect |
| 14. C3×H(3,𝔽3)×C31 | C32 | semidirect |
| 17. C33×C31 | C33 | semidirect |
| 23. C32×C31⋊C3 | H(3,𝔽3) | semidirect |
| 26. C32×C31⋊C3 | C33 | semidirect |
| 34. C32×C31 | C3×H(3,𝔽3) | semidirect |
| 42. C3×C31⋊C3 | C3×H(3,𝔽3) | semidirect |
| 47. C32⋊H(3,𝔽3) | C31⋊C3 | direct (N × H) |
| 53. C31⋊C3 | C32⋊H(3,𝔽3) | direct (N × H) |
| 58. C34 | C3×C31⋊C3 | semidirect |
| 62. C3×H(3,𝔽3) | C3×C31⋊C3 | semidirect |
| 63. C31 | C3×C32⋊H(3,𝔽3) | semidirect |
| 75. C33 | C32×C31⋊C3 | semidirect |
| 89. C32 | H(3,𝔽3)×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C31⋊C3 | 3 |
| C3×H(3,𝔽3)×C31⋊C3 | 3 |
| #21419308 | 3 |
| (C3×C31⋊C3)⋊H(3,𝔽3) | 3 |
| C31×C32⋊H(3,𝔽3) | 3 |
| C3×C32⋊H(3,𝔽3) | 31 |