Finite Group DatabasebetaFinite Group DatabasebetaOrder 6048.
1536 conjugacy classes of subgroups; only the 303 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 303 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 |
|---|---|---|
| 1. C32×C42×ΓL(1,𝔽8) | C2 | semidirect |
| 2. C7×#64083 | C3 | semidirect |
| 3. C2×ΓL(1,𝔽8)×C4⋊(C3⋊D3) | C2 | semidirect |
| 8. C2×C7×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 10. C32×C42×C7 | C2×C3 | semidirect |
| 12. C3×C42×ΓL(1,𝔽8) | D3 | semidirect |
| 16. C32×C4×ΓL(1,𝔽8) | D4 | semidirect |
| 32. C3×C42×C7 | C3×D3 | semidirect |
| 34. C42×ΓL(1,𝔽8) | C3⋊D3 | semidirect |
| 35. #64083 | ΓL(1,𝔽8) | direct (N × H) |
| 42. C32×C4×C7 | C3×D4 | semidirect |
| 44. C3×C4×ΓL(1,𝔽8) | D12 | semidirect |
| 49. C32×ΓL(1,𝔽8) | #127 | semidirect |
| 57. C2×C4⋊(C3⋊D3) | C2×ΓL(1,𝔽8) | semidirect |
| 61. C32×C42 | C2×ΓL(1,𝔽8) | semidirect |
| 68. C42×C7 | C3×C3⋊D3 | semidirect |
| 79. C3×C4×C7 | C3×D12 | semidirect |
| 81. C4×ΓL(1,𝔽8) | C4⋊(C3⋊D3) | semidirect |
| 89. C32×C7 | C3×#127 | semidirect |
| 91. C3×ΓL(1,𝔽8) | #874 | semidirect |
| 101. C3×C42 | D3×ΓL(1,𝔽8) | semidirect |
| 114. C32×C4 | D4×ΓL(1,𝔽8) | semidirect |
| 118. C4×C7 | C3×C4⋊(C3⋊D3) | semidirect |
| 127. C3×C7 | C3×#874 | semidirect |
| 129. ΓL(1,𝔽8) | #64083 | direct (N × H) |
| 136. C42 | C3⋊D3×ΓL(1,𝔽8) | semidirect |
| 146. C3×C4 | ΓL(1,𝔽8)×D12 | semidirect |
| 149. C32 | ΓL(1,𝔽8)×#127 | semidirect |
| 153. C7 | C3×#64083 | semidirect |
| 161. C4 | ΓL(1,𝔽8)×C4⋊(C3⋊D3) | semidirect |
| 164. C3 | ΓL(1,𝔽8)×#874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C42×ΓL(1,𝔽8) | 2 |
| C7×#64083 | 3 |
| C2×ΓL(1,𝔽8)×C4⋊(C3⋊D3) | 2 |
| ΓL(1,𝔽8)×#874 | 3 |
| C3×#64083 | 7 |