Finite Group DatabasebetaFinite Group Databasebeta← C7×C3⋊(C3⋊(C7⋊#261)) #37525631
Order 22932.
216 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊(C3⋊(C7⋊#261)) |
| commutator, hypocenter | C32×C7×C13 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C13 | C4 |
| prime radical | C32×C72×D13 | C2 |
| cosocle | C32×C7×D13 | C2×C7 |
| LCS | G ▷ C32×C7×C13 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×C72×C13 | C4 | semidirect |
| 5. C3⋊(C3⋊(C7⋊#261)) | C7 | direct (N × H) |
| 8. C3×C72×C13 | Dic3 | semidirect |
| 18. C32×C7×C13 | Dic7 | semidirect |
| 19. C32×C7×C13 | C4×C7 | semidirect |
| 20. C72×C13 | C3⋊Dic3 | semidirect |
| 26. C32×C72 | #261 | semidirect |
| 31. C3×C7×C13 | C7×Dic3 | semidirect |
| 32. C3×C7×C13 | Dic21 | semidirect |
| 41. C3×C72 | C3⋊#261 | semidirect |
| 45. C32×C13 | C7×Dic7 | semidirect |
| 48. C7×C13 | C7×C3⋊Dic3 | semidirect |
| 49. C7×C13 | C3⋊Dic21 | semidirect |
| 54. C32×C7 | C7×#261 | semidirect |
| 55. C32×C7 | C7⋊#261 | semidirect |
| 57. C72 | C3⋊(C3⋊#261) | semidirect |
| 61. C3×C13 | C7×Dic21 | semidirect |
| 67. C3×C7 | C7×C3⋊#261 | semidirect |
| 68. C3×C7 | C3⋊(C7⋊#261) | semidirect |
| 73. C13 | C7×C3⋊Dic21 | semidirect |
| 75. C32 | C7×C7⋊#261 | semidirect |
| 77. C7 | C7×C3⋊(C3⋊#261) | semidirect |
| 78. C7 | C3⋊(C3⋊(C7⋊#261)) | direct (N × H) |
| 81. C3 | C7×C3⋊(C7⋊#261) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C72×D13 | 2 |
| C7×C3⋊(C7⋊#261) | 3 |
| C3⋊(C3⋊(C7⋊#261)) | 7 |
| C7×C3⋊(C3⋊#261) | 7 |
| C7×C3⋊Dic21 | 13 |