Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
352 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 6. C3×C4×SL(2,𝔽3) | C4 | semidirect |
| 7. C3×C4×SL(2,𝔽3) | C4 | semidirect |
| 34. C4×SL(2,𝔽3) | Dic3 | semidirect |
| 35. C4×SL(2,𝔽3) | Dic3 | semidirect |
| 46. C3×SL(2,𝔽3) | C4⋊C4 | semidirect |
| 125. SL(2,𝔽3) | C4⋊Dic3 | semidirect |
| 169. C3×C4 | GU(2,𝔽3) | semidirect |
| 215. C4 | C3⋊GU(2,𝔽3) | semidirect |
| 219. C3 | C4⋊GU(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#41⋊C3 | 2 |
| C2×C3⋊GU(2,𝔽3) | 2 |
| C4⋊GU(2,𝔽3) | 3 |
| #71646 | 3 |
| C4⋊(C3⋊(C3⋊C8)) | 4 |