Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
360 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 150 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 |
|---|---|---|
| 5. C3×#4493 | C3 | direct (N × H) |
| 23. #4493 | C32 | direct (N × H) |
| 83. C33 | #368 | semidirect |
| 118. C32 | #4493 | direct (N × H) |
| 119. C32 | C3×#368 | semidirect |
| 135. C3 | C3×#4493 | direct (N × H) |
| 136. C3 | C32×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#108 | 2 |
| C32×#819 | 2 |
| C2×C32×C3⋊C16 | 2 |
| C32×#368 | 3 |
| C3×#4493 | 3 |