Finite Group DatabasebetaFinite Group Databasebeta← C32×C11×C7⋊AGL(1,𝔽5) #28357652
Order 13860.
144 conjugacy classes of subgroups.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C11×C7⋊AGL(1,𝔽5) | C3 | direct (N × H) |
| 3. C32×C5×C7×C11 | C4 | semidirect |
| 7. C11×C7⋊AGL(1,𝔽5) | C32 | direct (N × H) |
| 9. C32×C7⋊AGL(1,𝔽5) | C11 | direct (N × H) |
| 10. C3×C5×C7×C11 | C3×C4 | semidirect |
| 14. C32×C7×C11 | AGL(1,𝔽5) | semidirect |
| 17. C32×C5×C11 | Dic7 | semidirect |
| 19. C3×C7⋊AGL(1,𝔽5) | C3×C11 | direct (N × H) |
| 21. C5×C7×C11 | C32×C4 | semidirect |
| 23. C32×C5×C7 | C4×C11 | semidirect |
| 26. C3×C7×C11 | C3×AGL(1,𝔽5) | semidirect |
| 31. C3×C5×C11 | C3×Dic7 | semidirect |
| 33. C7⋊AGL(1,𝔽5) | C32×C11 | direct (N × H) |
| 37. C3×C5×C7 | C3×C4×C11 | semidirect |
| 38. C32×C11 | C7⋊AGL(1,𝔽5) | direct (N × H) |
| 41. C7×C11 | C32×AGL(1,𝔽5) | semidirect |
| 44. C32×C7 | C11×AGL(1,𝔽5) | semidirect |
| 46. C5×C11 | C32×Dic7 | semidirect |
| 47. C32×C5 | C11×Dic7 | semidirect |
| 51. C5×C7 | C32×C4×C11 | semidirect |
| 52. C3×C11 | C3×C7⋊AGL(1,𝔽5) | direct (N × H) |
| 56. C3×C7 | C3×C11×AGL(1,𝔽5) | semidirect |
| 59. C3×C5 | C3×C11×Dic7 | semidirect |
| 62. C11 | C32×C7⋊AGL(1,𝔽5) | direct (N × H) |
| 64. C32 | C11×C7⋊AGL(1,𝔽5) | direct (N × H) |
| 65. C7 | C32×C11×AGL(1,𝔽5) | semidirect |
| 67. C5 | C32×C11×Dic7 | semidirect |
| 69. C3 | C3×C11×C7⋊AGL(1,𝔽5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C7×D5×C11 | 2 |
| C3×C11×C7⋊AGL(1,𝔽5) | 3 |
| C32×C11×Dic7 | 5 |
| C32×C11×AGL(1,𝔽5) | 7 |
| C32×C7⋊AGL(1,𝔽5) | 11 |