Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
752 conjugacy classes of subgroups; only the 402 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 402 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. C32×#812 | C2 | semidirect |
| 3. C2×C32×C3⋊C16 | C2 | semidirect |
| 5. C3×#5140 | C3 | direct (N × H) |
| 16. C3×#812 | C2×C3 | semidirect |
| 17. C2×C3×C3⋊C16 | C2×C3 | semidirect |
| 24. #5140 | C32 | direct (N × H) |
| 46. #812 | C2×C32 | semidirect |
| 47. C2×C3⋊C16 | C2×C32 | semidirect |
| 91. C33 | #504 | semidirect |
| 128. C32 | #5140 | direct (N × H) |
| 129. C32 | C3×#504 | semidirect |
| 145. C3 | C3×#5140 | direct (N × H) |
| 146. C3 | C32×#504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#131 | 2 |
| C32×#812 | 2 |
| C2×C32×C3⋊C16 | 2 |
| C32×#504 | 3 |
| C3×#5140 | 3 |