Finite Group DatabasebetaFinite Group DatabasebetaOrder 1512.
192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 4. C3×#4248 | C3 | semidirect |
| 6. #4248⋊C3 | C3 | direct (N × H) |
| 20. C32×ΓL(1,𝔽8) | Q8 | semidirect |
| 22. #4248 | C32 | semidirect |
| 46. C32×C7 | C3×Q8 | semidirect |
| 49. C3×ΓL(1,𝔽8) | Dic6 | semidirect |
| 50. C3×ΓL(1,𝔽8) | C3×Q8 | semidirect |
| 77. C3×C7 | C3×Dic6 | semidirect |
| 78. C3×C7 | C32×Q8 | semidirect |
| 80. ΓL(1,𝔽8) | C3×Dic6 | semidirect |
| 102. C32 | ΓL(1,𝔽8)⋊Q8 | semidirect |
| 104. C7 | C32×Dic6 | semidirect |
| 116. C3 | #4248⋊C3 | direct (N × H) |
| 117. C3 | C3×ΓL(1,𝔽8)⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C3⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| C3×Dic3×ΓL(1,𝔽8) | 2 |
| C32×ΓL(1,𝔽8)⋊C4 | 2 |
| C3×#4248 | 3 |
| C3×ΓL(1,𝔽8)⋊Q8 | 3 |
| #4248⋊C3 | 3 |
| C32×Dic6 | 7 |