Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
752 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 282 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×C4×C8 | C2 | semidirect |
| 4. C32×Dic3⋊C8 | C2 | semidirect |
| 5. C32×#803 | C2 | semidirect |
| 7. C3×#4690 | C3 | direct (N × H) |
| 21. C32×C4×C8 | D3 | semidirect |
| 22. C32×C4×C8 | C2×C3 | semidirect |
| 24. C3×Dic3⋊C8 | C2×C3 | semidirect |
| 25. C3×#803 | C2×C3 | semidirect |
| 35. #4690 | C32 | direct (N × H) |
| 65. C3×C4×C8 | C3×D3 | semidirect |
| 66. C3×C4×C8 | C2×C32 | semidirect |
| 68. Dic3⋊C8 | C2×C32 | semidirect |
| 69. #803 | C2×C32 | semidirect |
| 130. C4×C8 | C32×D3 | semidirect |
| 131. C33 | #433 | semidirect |
| 184. C32 | #4690 | direct (N × H) |
| 185. C32 | C3×#433 | semidirect |
| 210. C3 | C3×#4690 | direct (N × H) |
| 211. C3 | C32×#433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#872 | 2 |
| C33×C4×C8 | 2 |
| C32×(C2×D3)⋊C8 | 2 |
| C32×Dic3⋊C8 | 2 |
| C32×#803 | 2 |
| C32×#433 | 3 |
| C3×#4690 | 3 |