Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
580 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 90 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×#4181 | C2 | semidirect |
| 2. C3×C4×C32⋊C9 | C2 | semidirect |
| 5. C4⋊#4181 | C3 | direct (N × H) |
| 11. C32×C4×C9 | D3 | semidirect |
| 12. C2×#4181 | C2×C3 | semidirect |
| 15. C4×C32⋊C9 | C2×C3 | semidirect |
| 16. C3×C32⋊C9 | D4 | semidirect |
| 39. C33×C4 | D9 | semidirect |
| 46. C3×C4×C9 | C3×D3 | semidirect |
| 48. C32×C9 | D12 | semidirect |
| 51. C32⋊C9 | C3×D4 | semidirect |
| 90. C32×C4 | C3×D9 | semidirect |
| 101. C33 | D36 | semidirect |
| 106. C3×C9 | C3×D12 | semidirect |
| 141. C3×C4 | #4181 | semidirect |
| 153. C32 | C3×D36 | semidirect |
| 172. C4 | C3×#4181 | semidirect |
| 177. C3 | C4⋊#4181 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#4181 | 2 |
| C3×C4×C32⋊C9 | 2 |
| C32×C4⋊(C3⋊D3) | 3 |
| C32×D36 | 3 |
| C4⋊#4181 | 3 |