Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
956 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 956 conjugacy classes of subgroups — too many to draw. Only its 238 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×#3746 | C2 | semidirect |
| 3. C2×C3×#3744 | C2 | semidirect |
| 4. C3×#64084 | C2 | semidirect |
| 5. C33×C4×C8 | C2 | semidirect |
| 6. #10592395 | C3 | direct (N × H) |
| 17. C2×#3746 | C2×C3 | semidirect |
| 19. C2×#3744 | C2×C3 | semidirect |
| 20. #64084 | C2×C3 | semidirect |
| 26. C32×C4×C8 | D3 | semidirect |
| 27. C32×C4×C8 | C2×C3 | semidirect |
| 77. C3×C4×C8 | C3×D3 | semidirect |
| 78. C3×C4×C8 | C3⋊D3 | semidirect |
| 150. C4×C8 | C3×C3⋊D3 | semidirect |
| 151. C33 | #495 | semidirect |
| 212. C32 | #4696 | semidirect |
| 213. C32 | C3×#495 | semidirect |
| 240. C3 | C3×#4696 | semidirect |
| 241. C3 | #10592395 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3746 | 2 |
| C2×C3×#3745 | 2 |
| C2×C3×#3744 | 2 |
| C3×#64084 | 2 |
| C33×C4×C8 | 2 |
| #10592395 | 3 |
| C3×#4696 | 3 |