Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1004 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1004 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×#944 | C2 | semidirect |
| 3. C32×#909 | C2 | semidirect |
| 4. C33×#101 | C2 | semidirect |
| 5. C32×#825 | C2 | semidirect |
| 7. C3×#4752 | C3 | direct (N × H) |
| 23. C3×#944 | C2×C3 | semidirect |
| 24. C3×#909 | C2×C3 | semidirect |
| 27. C32×#101 | D3 | semidirect |
| 28. C32×#101 | C2×C3 | semidirect |
| 29. C3×#825 | C2×C3 | semidirect |
| 45. #4752 | C32 | direct (N × H) |
| 81. #944 | C2×C32 | semidirect |
| 82. #909 | C2×C32 | semidirect |
| 85. C3×#101 | C3×D3 | semidirect |
| 86. C3×#101 | C2×C32 | semidirect |
| 87. #825 | C2×C32 | semidirect |
| 169. #101 | C32×D3 | semidirect |
| 170. C33 | #456 | semidirect |
| 240. C32 | #4752 | direct (N × H) |
| 241. C32 | C3×#456 | semidirect |
| 272. C3 | C3×#4752 | direct (N × H) |
| 273. C3 | C32×#456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1007 | 2 |
| C32×#944 | 2 |
| C32×#909 | 2 |
| C33×#101 | 2 |
| C32×#825 | 2 |
| C32×#456 | 3 |
| C3×#4752 | 3 |