Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
880 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 234 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. C32×#870 | C2 | semidirect |
| 3. C32×#835 | C2 | semidirect |
| 5. C32×C4×C3⋊C8 | C2 | semidirect |
| 7. C3×#5056 | C3 | direct (N × H) |
| 19. C3×#870 | C2×C3 | semidirect |
| 23. C3×#835 | C2×C3 | semidirect |
| 25. C3×C4×C3⋊C8 | C2×C3 | semidirect |
| 35. #5056 | C32 | direct (N × H) |
| 65. #870 | C2×C32 | semidirect |
| 69. #835 | C2×C32 | semidirect |
| 71. C4×C3⋊C8 | C2×C32 | semidirect |
| 141. C33 | #488 | semidirect |
| 201. C32 | #5056 | direct (N × H) |
| 202. C32 | C3×#488 | semidirect |
| 228. C3 | C3×#5056 | direct (N × H) |
| 229. C3 | C32×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#124 | 2 |
| C32×#870 | 2 |
| C32×#835 | 2 |
| C32×#832 | 2 |
| C32×C4×C3⋊C8 | 2 |
| C32×#488 | 3 |
| C3×#5056 | 3 |