Finite Group DatabasebetaFinite Group DatabasebetaOrder 32634.
240 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C37⋊C3×#3861 |
| commutator, cosocle, hypocenter | C72×C37 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C37 | C32 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C37⋊C3×#3861 | C2 | direct (N × H) |
| 2. C2×C72×C37⋊C3 | C3 | semidirect |
| 3. C2×C37×#3861 | C3 | semidirect |
| 4. C2×#19129588 | C3 | semidirect |
| 5. C2×#19129589 | C3 | semidirect |
| 6. #19129589 | C2×C3 | semidirect |
| 7. #19129588 | C2×C3 | semidirect |
| 8. C37×#3861 | C2×C3 | semidirect |
| 9. C72×C37⋊C3 | C2×C3 | semidirect |
| 11. C2×C72×C37 | C32 | semidirect |
| 13. C72×C37 | C2×C32 | semidirect |
| 17. C2×C7×C37⋊C3 | ΓL(1,𝔽8) | semidirect |
| 21. C7×C37⋊C3 | C2×ΓL(1,𝔽8) | semidirect |
| 24. C2×C7×C37 | C3×ΓL(1,𝔽8) | semidirect |
| 30. C2×#3861 | C37⋊C3 | direct (N × H) |
| 31. C7×C37 | C2×C3×ΓL(1,𝔽8) | semidirect |
| 35. C2×C37⋊C3 | #3861 | direct (N × H) |
| 39. #3861 | C2×C37⋊C3 | direct (N × H) |
| 44. C37⋊C3 | C2×#3861 | direct (N × H) |
| 45. C2×C72 | C3×C37⋊C3 | semidirect |
| 46. C2×C37 | C3×#3861 | semidirect |
| 48. C72 | C2×C3×C37⋊C3 | semidirect |
| 53. C37 | C2×C3×#3861 | semidirect |
| 59. C2×C7 | ΓL(1,𝔽8)×C37⋊C3 | semidirect |
| 61. C7 | C2×ΓL(1,𝔽8)×C37⋊C3 | semidirect |
| 70. C2 | C37⋊C3×#3861 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37⋊C3×#3861 | 2 |
| C2×C72×C37⋊C3 | 3 |
| C2×C37×#3861 | 3 |
| C2×#19129588 | 3 |
| C2×#19129589 | 3 |
| C2×ΓL(1,𝔽8)×C37⋊C3 | 7 |
| C2×C3×#3861 | 37 |