Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
800 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 190 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. C33×#125 | C2 | semidirect |
| 3. C3×#63637 | C2 | semidirect |
| 5. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 6. #10592767 | C3 | direct (N × H) |
| 16. C32×#125 | D3 | semidirect |
| 17. C32×#125 | C2×C3 | semidirect |
| 20. #63637 | C2×C3 | semidirect |
| 22. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 61. C3×#125 | C3×D3 | semidirect |
| 62. C3×#125 | C3⋊D3 | semidirect |
| 129. #125 | C3×C3⋊D3 | semidirect |
| 134. C33 | #488 | semidirect |
| 188. C32 | #5068 | semidirect |
| 189. C32 | C3×#488 | semidirect |
| 214. C3 | C3×#5068 | semidirect |
| 215. C3 | #10592767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#125 | 2 |
| C3×#64084 | 2 |
| C3×#63637 | 2 |
| C3×#63636 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| #10592767 | 3 |
| C3×#5068 | 3 |