Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×C3⋊(ΓL(1,𝔽8)⋊C4) #13094749
Order 1512.
272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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×C3⋊(ΓL(1,𝔽8)⋊C4) | C2 | direct (N × H) |
| 3. C2×C3×Dic21 | C3 | semidirect |
| 4. C2×C3⋊(ΓL(1,𝔽8)⋊C4) | C3 | direct (N × H) |
| 6. C2×C32×ΓL(1,𝔽8) | C4 | semidirect |
| 13. C3×Dic21 | C2×C3 | semidirect |
| 14. C3⋊(ΓL(1,𝔽8)⋊C4) | C2×C3 | direct (N × H) |
| 17. C32×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 18. C2×Dic21 | C32 | semidirect |
| 21. C2×C32×C7 | C3×C4 | semidirect |
| 27. C2×C3×ΓL(1,𝔽8) | Dic3 | semidirect |
| 28. C2×C3×ΓL(1,𝔽8) | C3×C4 | semidirect |
| 38. Dic21 | C2×C32 | semidirect |
| 44. C32×C7 | C2×C3×C4 | semidirect |
| 47. C3×ΓL(1,𝔽8) | C2×Dic3 | semidirect |
| 48. C3×ΓL(1,𝔽8) | C2×C3×C4 | semidirect |
| 54. C2×C3×C7 | C3×Dic3 | semidirect |
| 55. C2×C3×C7 | C32×C4 | semidirect |
| 60. C2×ΓL(1,𝔽8) | C3×Dic3 | semidirect |
| 77. C3×C7 | C2×C3×Dic3 | semidirect |
| 78. C3×C7 | C2×C32×C4 | semidirect |
| 80. ΓL(1,𝔽8) | C2×C3×Dic3 | semidirect |
| 89. C2×C32 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 91. C2×C7 | C32×Dic3 | semidirect |
| 105. C32 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 107. C7 | C2×C32×Dic3 | semidirect |
| 114. C2×C3 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 115. C2×C3 | C3⋊(ΓL(1,𝔽8)⋊C4) | direct (N × H) |
| 123. C3 | C2×C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 124. C3 | C2×C3⋊(ΓL(1,𝔽8)⋊C4) | direct (N × H) |
| 125. C2 | C3×C3⋊(ΓL(1,𝔽8)⋊C4) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×ΓL(1,𝔽8) | 2 |
| C3×C3⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| C2×C3×Dic21 | 3 |
| C2×C3⋊(ΓL(1,𝔽8)⋊C4) | 3 |
| C2×C3×ΓL(1,𝔽8)⋊C4 | 3 |
| C2×C32×Dic3 | 7 |