Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
720 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 222 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. C2×C32×Dic12 | C2 | semidirect |
| 4. C33×#108 | C2 | semidirect |
| 5. C32×#824 | C2 | semidirect |
| 7. C3×#4896 | C3 | direct (N × H) |
| 23. C2×C3×Dic12 | C2×C3 | semidirect |
| 26. C32×#108 | D3 | semidirect |
| 27. C32×#108 | C2×C3 | semidirect |
| 29. C3×#824 | C2×C3 | semidirect |
| 43. #4896 | C32 | direct (N × H) |
| 78. C2×Dic12 | C2×C32 | semidirect |
| 81. C3×#108 | C3×D3 | semidirect |
| 82. C3×#108 | C2×C32 | semidirect |
| 84. #824 | C2×C32 | semidirect |
| 159. #108 | C32×D3 | semidirect |
| 161. C33 | #473 | semidirect |
| 225. C32 | #4896 | direct (N × H) |
| 226. C32 | C3×#473 | semidirect |
| 254. C3 | C3×#4896 | direct (N × H) |
| 255. C3 | C32×#473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#909 | 2 |
| C2×C32×Dic12 | 2 |
| C32×#901 | 2 |
| C33×#108 | 2 |
| C32×#824 | 2 |
| C32×#473 | 3 |
| C3×#4896 | 3 |