Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
596 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 210 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 |
|---|---|---|
| 1. C2×C32×Dic12 | C2 | semidirect |
| 3. C33×M32 | C2 | semidirect |
| 4. C32×Dic24 | C2 | semidirect |
| 5. C32×#800 | C2 | semidirect |
| 7. C3×#4909 | C3 | direct (N × H) |
| 19. C2×C3×Dic12 | C2×C3 | semidirect |
| 24. C32×M32 | D3 | semidirect |
| 25. C32×M32 | C2×C3 | semidirect |
| 26. C3×Dic24 | C2×C3 | semidirect |
| 27. C3×#800 | C2×C3 | semidirect |
| 39. #4909 | C32 | direct (N × H) |
| 68. C2×Dic12 | C2×C32 | semidirect |
| 73. C3×M32 | C3×D3 | semidirect |
| 74. C3×M32 | C2×C32 | semidirect |
| 75. Dic24 | C2×C32 | semidirect |
| 76. #800 | C2×C32 | semidirect |
| 143. M32 | C32×D3 | semidirect |
| 144. C33 | #510 | semidirect |
| 201. C32 | #4909 | direct (N × H) |
| 202. C32 | C3×#510 | semidirect |
| 228. C3 | C3×#4909 | direct (N × H) |
| 229. C3 | C32×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Dic12 | 2 |
| C32×#904 | 2 |
| C33×M32 | 2 |
| C32×Dic24 | 2 |
| C32×#800 | 2 |
| C32×#510 | 3 |
| C3×#4909 | 3 |