Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
492 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 2. C33×#108 | C2 | semidirect |
| 3. C32×#812 | C2 | semidirect |
| 5. C3×#4495 | C3 | direct (N × H) |
| 16. C32×#108 | D3 | semidirect |
| 17. C32×#108 | C2×C3 | semidirect |
| 18. C3×#812 | C2×C3 | semidirect |
| 27. #4495 | C32 | direct (N × H) |
| 51. C3×#108 | C3×D3 | semidirect |
| 52. C3×#108 | C2×C32 | semidirect |
| 53. #812 | C2×C32 | semidirect |
| 105. #108 | C32×D3 | semidirect |
| 106. C33 | #361 | semidirect |
| 153. C32 | #4495 | direct (N × H) |
| 154. C32 | C3×#361 | semidirect |
| 176. C3 | C3×#4495 | direct (N × H) |
| 177. C3 | C32×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D24 | 2 |
| C33×#108 | 2 |
| C32×#812 | 2 |
| C32×#361 | 3 |
| C3×#4495 | 3 |