Finite Group DatabasebetaFinite Group DatabasebetaOrder 7533.
166 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C31⋊C3 |
| commutator, socle | C32×C31 | C33 |
| Fitting | C31×C32⋊C9 | C3 |
| hypercenter | C32⋊C9 | C31⋊C3 |
| hypocenter | C31 | C9⋊H(3,𝔽3) |
| LCS | G ▷ C32×C31 ▷ C31 | |
| UCS | C1 ◁ C32 ◁ C32⋊C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#11719689 | C3 | semidirect |
| 2. C3×#11719686 | C3 | semidirect |
| 3. C3×#11719687 | C3 | semidirect |
| 5. C3×C9×C31⋊C3 | C3 | semidirect |
| 6. C32⋊(C31⋊C9) | C3 | semidirect |
| 7. (C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 8. (C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 9. (C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 10. (C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 11. (C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 12. (C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 13. C31×C32⋊C9 | C3 | semidirect |
| 48. C3×C31⋊C3 | 3−1+2 | semidirect |
| 57. C31⋊C9 | H(3,𝔽3) | semidirect |
| 79. C32⋊C9 | C31⋊C3 | semidirect |
| 80. C31 | C9⋊H(3,𝔽3) | semidirect |