Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
308 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C3×#4179 | C2 | semidirect |
| 2. C3×C4×#732 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊D9) | C3 | semidirect |
| 5. C4⋊#4179 | C3 | direct (N × H) |
| 8. C2×C3×C3⋊D9 | C2×C3 | semidirect |
| 12. C32×C4×C9 | C2×C3 | semidirect |
| 13. C2×#4179 | C2×C3 | semidirect |
| 15. C4×#732 | C2×C3 | semidirect |
| 16. C3×#732 | D4 | semidirect |
| 19. C4⋊(C3⋊D9) | C32 | semidirect |
| 35. C2×C3⋊D9 | C2×C32 | semidirect |
| 45. C3×C4×C9 | C2×C32 | semidirect |
| 48. C32×C9 | C3×D4 | semidirect |
| 50. #732 | C3×D4 | semidirect |
| 102. C3×C9 | C32×D4 | semidirect |
| 135. C3×C4 | #4179 | semidirect |
| 163. C4 | C3×#4179 | semidirect |
| 169. C3 | C4⋊#4179 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#4179 | 2 |
| C3×C4×#732 | 2 |
| C3×C4⋊(C3⋊D9) | 3 |
| C3×C4⋊((C3⋊D3)⋊C3) | 3 |
| C4⋊#4179 | 3 |