Finite Group DatabasebetaFinite Group Databasebeta← C3⋊(ΓL(1,𝔽8)⋊Dic133) #45691929
Order 33516.
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 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. C3⋊(C7⋊Dic133) | C3 | semidirect |
| 4. C3×C7×C19×ΓL(1,𝔽8) | C4 | semidirect |
| 12. C7×C19×ΓL(1,𝔽8) | Dic3 | semidirect |
| 13. C3×C72×C19 | C3×C4 | semidirect |
| 24. C3×C19×ΓL(1,𝔽8) | Dic7 | semidirect |
| 25. C72×C19 | C3×Dic3 | semidirect |
| 40. C3×C7×ΓL(1,𝔽8) | Dic19 | semidirect |
| 44. C3×C7×C19 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 45. C3×C7×C19 | C3×Dic7 | semidirect |
| 47. C19×ΓL(1,𝔽8) | Dic21 | semidirect |
| 61. C3×C72 | C3×Dic19 | semidirect |
| 63. C7×ΓL(1,𝔽8) | Dic57 | semidirect |
| 65. C7×C19 | C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 66. C7×C19 | C3×Dic21 | semidirect |
| 80. C3×ΓL(1,𝔽8) | Dic133 | semidirect |
| 83. C3×C19 | ΓL(1,𝔽8)⋊Dic7 | semidirect |
| 84. C72 | C3×Dic57 | semidirect |
| 100. C3×C7 | ΓL(1,𝔽8)⋊Dic19 | semidirect |
| 101. C3×C7 | C3×Dic133 | semidirect |
| 103. ΓL(1,𝔽8) | Dic399 | semidirect |
| 104. C19 | C3⋊(ΓL(1,𝔽8)⋊Dic7) | semidirect |
| 113. C7 | C3⋊(ΓL(1,𝔽8)⋊Dic19) | semidirect |
| 114. C7 | C3×Dic399 | semidirect |
| 121. C3 | ΓL(1,𝔽8)⋊Dic133 | 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 |
| C3⋊(C7⋊Dic133) | 3 |
| ΓL(1,𝔽8)⋊Dic133 | 3 |
| C3×Dic399 | 7 |
| C3⋊(ΓL(1,𝔽8)⋊Dic19) | 7 |
| C3⋊(ΓL(1,𝔽8)⋊Dic7) | 19 |