Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
448 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 162 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×C33×C16 | C2 | semidirect |
| 3. C32×#812 | C2 | semidirect |
| 5. C3×#4508 | C3 | direct (N × H) |
| 17. C2×C32×C16 | D3 | semidirect |
| 18. C2×C32×C16 | C2×C3 | semidirect |
| 19. C3×#812 | C2×C3 | semidirect |
| 29. #4508 | C32 | direct (N × H) |
| 55. C2×C3×C16 | C3×D3 | semidirect |
| 56. C2×C3×C16 | C2×C32 | semidirect |
| 57. #812 | C2×C32 | semidirect |
| 112. C2×C16 | C32×D3 | semidirect |
| 113. C33 | #350 | semidirect |
| 162. C32 | #4508 | direct (N × H) |
| 163. C32 | C3×#350 | semidirect |
| 186. C3 | C3×#4508 | direct (N × H) |
| 187. C3 | C32×#350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#901 | 2 |
| C2×C33×C16 | 2 |
| C32×#812 | 2 |
| C32×#350 | 3 |
| C3×#4508 | 3 |