Finite Group DatabasebetaFinite Group Databasebeta← C7×C3⋊(C3⋊(C7⋊#595)) #44472983
Order 29988.
216 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊(C3⋊(C7⋊#595)) |
| commutator, hypocenter | C32×C7×C17 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C17 | C4 |
| prime radical | C32×C72×D17 | C2 |
| cosocle | C32×C7×D17 | C2×C7 |
| LCS | G ▷ C32×C7×C17 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×C72×C17 | C4 | semidirect |
| 5. C3⋊(C3⋊(C7⋊#595)) | C7 | direct (N × H) |
| 8. C3×C72×C17 | Dic3 | semidirect |
| 17. C32×C7×C17 | Dic7 | semidirect |
| 18. C32×C7×C17 | C4×C7 | semidirect |
| 20. C72×C17 | C3⋊Dic3 | semidirect |
| 28. C32×C72 | #595 | semidirect |
| 30. C3×C7×C17 | C7×Dic3 | semidirect |
| 31. C3×C7×C17 | Dic21 | semidirect |
| 41. C32×C17 | C7×Dic7 | semidirect |
| 42. C3×C72 | C3⋊#595 | semidirect |
| 47. C7×C17 | C7×C3⋊Dic3 | semidirect |
| 48. C7×C17 | C3⋊Dic21 | semidirect |
| 55. C32×C7 | C7×#595 | semidirect |
| 56. C32×C7 | C7⋊#595 | semidirect |
| 57. C3×C17 | C7×Dic21 | semidirect |
| 58. C72 | C3⋊(C3⋊#595) | semidirect |
| 67. C3×C7 | C7×C3⋊#595 | semidirect |
| 68. C3×C7 | C3⋊(C7⋊#595) | semidirect |
| 70. C17 | C7×C3⋊Dic21 | semidirect |
| 75. C32 | C7×C7⋊#595 | semidirect |
| 77. C7 | C7×C3⋊(C3⋊#595) | semidirect |
| 78. C7 | C3⋊(C3⋊(C7⋊#595)) | direct (N × H) |
| 81. C3 | C7×C3⋊(C7⋊#595) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C72×D17 | 2 |
| C7×C3⋊(C7⋊#595) | 3 |
| C3⋊(C3⋊(C7⋊#595)) | 7 |
| C7×C3⋊(C3⋊#595) | 7 |
| C7×C3⋊Dic21 | 17 |