Finite Group DatabasebetaFinite Group Databasebeta← C7×C3⋊(ΓL(1,𝔽8)⋊Dic19) #45691893
Order 33516.
120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×Dic399 | C3 | semidirect |
| 4. C3×C7×C19×ΓL(1,𝔽8) | C4 | semidirect |
| 9. C3⋊(ΓL(1,𝔽8)⋊Dic19) | C7 | direct (N × H) |
| 12. C7×C19×ΓL(1,𝔽8) | Dic3 | semidirect |
| 13. C3×C72×C19 | C3×C4 | semidirect |
| 18. Dic399 | C3×C7 | semidirect |
| 23. C3×C19×ΓL(1,𝔽8) | C4×C7 | semidirect |
| 24. C72×C19 | C3×Dic3 | semidirect |
| 38. C3×C7×ΓL(1,𝔽8) | Dic19 | semidirect |
| 42. C3×C7×C19 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 43. C3×C7×C19 | C3×C4×C7 | semidirect |
| 45. C19×ΓL(1,𝔽8) | C7×Dic3 | semidirect |
| 59. C3×C72 | C3×Dic19 | semidirect |
| 61. C7×ΓL(1,𝔽8) | Dic57 | semidirect |
| 63. C7×C19 | C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 64. C7×C19 | C3×C7×Dic3 | semidirect |
| 77. C3×ΓL(1,𝔽8) | C7×Dic19 | semidirect |
| 80. C3×C19 | C7×ΓL(1,𝔽8)⋊C4 | semidirect |
| 81. C72 | C3×Dic57 | semidirect |
| 96. C3×C7 | ΓL(1,𝔽8)⋊Dic19 | semidirect |
| 97. C3×C7 | C3×C7×Dic19 | semidirect |
| 99. ΓL(1,𝔽8) | C7×Dic57 | semidirect |
| 100. C19 | C7×C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 109. C7 | C3⋊(ΓL(1,𝔽8)⋊Dic19) | direct (N × H) |
| 110. C7 | C3×C7×Dic57 | semidirect |
| 117. C3 | C7×ΓL(1,𝔽8)⋊Dic19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C19×ΓL(1,𝔽8) | 2 |
| C7×Dic399 | 3 |
| C7×ΓL(1,𝔽8)⋊Dic19 | 3 |
| C3×C7×Dic57 | 7 |
| C3⋊(ΓL(1,𝔽8)⋊Dic19) | 7 |
| C7×C3⋊(ΓL(1,𝔽8)⋊C4) | 19 |