Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
671 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 671 conjugacy classes of subgroups — too many to draw. Only its 136 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×C4×C32⋊C9 | C2 | semidirect |
| 3. C3⋊#66316 | C2 | semidirect |
| 5. C4×C3⋊(C3⋊D9) | C3 | semidirect |
| 8. C3⋊#4169 | C4 | direct (N × H) |
| 14. C32×C4×C9 | C2×C3 | semidirect |
| 15. C3⋊(C3⋊Dic9) | C2×C3 | semidirect |
| 18. C4×C32⋊C9 | D3 | semidirect |
| 20. C3×C32⋊C9 | C2×C4 | semidirect |
| 32. C3⋊(C3⋊D9) | C3×C4 | semidirect |
| 45. C33×C4 | D9 | semidirect |
| 58. C3×C4×C9 | C3×D3 | semidirect |
| 63. C32×C9 | C2×C3×C4 | semidirect |
| 65. C32⋊C9 | C4×D3 | semidirect |
| 112. C32×C4 | C3⋊D9 | semidirect |
| 130. C33 | C4×D9 | semidirect |
| 136. C3×C9 | C3×C4×D3 | semidirect |
| 175. C3×C4 | #4169 | semidirect |
| 194. C32 | C4×C3⋊D9 | semidirect |
| 213. C4 | C3⋊#4169 | direct (N × H) |
| 217. C3 | C4×#4169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊#4169 | 2 |
| C3×C4×C32⋊C9 | 2 |
| C3⋊#66316 | 2 |
| C3×C4×C3⋊(C3⋊D3) | 3 |
| C4×C3⋊(C3⋊D9) | 3 |
| C4×#4169 | 3 |