Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
372 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 372 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×#4494 | C3 | direct (N × H) |
| 9. C32×C3⋊C16 | C4 | semidirect |
| 23. #4494 | C32 | direct (N × H) |
| 33. C3×C3⋊C16 | C3×C4 | semidirect |
| 71. C3⋊C16 | C32×C4 | semidirect |
| 86. C33 | #365 | semidirect |
| 123. C32 | #4494 | direct (N × H) |
| 124. C32 | C3×#365 | semidirect |
| 141. C3 | C3×#4494 | direct (N × H) |
| 142. C3 | C32×#365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#108 | 2 |
| C32×#817 | 2 |
| C32×#812 | 2 |
| C32×#365 | 3 |
| C3×#4494 | 3 |