Finite Group DatabasebetaFinite Group DatabasebetaOrder 37386.
36 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C3⋊(D67⋊C3) |
| commutator, cosocle, hypocenter | C3×C67 | C2×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C67 | C2×C3 |
| LCS | G ▷ C3×C67 | |
| UCS | C1 ◁ C31 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C31×C67⋊C3 | C2 | semidirect |
| 3. C31×D201 | C3 | semidirect |
| 4. C3×C31×C67 | C2×C3 | semidirect |
| 6. C31×C67⋊C3 | D3 | semidirect |
| 8. C31×C67 | C3×D3 | semidirect |
| 9. C3⋊(D67⋊C3) | C31 | direct (N × H) |
| 10. C3×C67⋊C3 | C2×C31 | semidirect |
| 12. D201 | C3×C31 | semidirect |
| 15. C3×C67 | C2×C3×C31 | semidirect |
| 17. C67⋊C3 | D3×C31 | semidirect |
| 23. C3×C31 | D67⋊C3 | semidirect |
| 24. C67 | C3×D3×C31 | semidirect |
| 26. C31 | C3⋊(D67⋊C3) | direct (N × H) |
| 33. C3 | C31×D67⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C31×C67⋊C3 | 2 |
| C31×D67⋊C3 | 3 |
| C31×D201 | 3 |
| C3⋊(D67⋊C3) | 31 |
| C3×D3×C31 | 67 |