Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
588 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 198 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×Q32 | C2 | semidirect |
| 3. C32×#829 | C2 | semidirect |
| 4. C32×Dic24 | C2 | semidirect |
| 7. C3×D3×Q32 | C3 | direct (N × H) |
| 20. C32×Q32 | D3 | direct (N × H) |
| 21. C32×Q32 | C2×C3 | semidirect |
| 23. C3×#829 | C2×C3 | semidirect |
| 24. C3×Dic24 | C2×C3 | semidirect |
| 34. D3×Q32 | C32 | direct (N × H) |
| 61. C3×Q32 | C3×D3 | direct (N × H) |
| 62. C3×Q32 | C2×C32 | semidirect |
| 64. #829 | C2×C32 | semidirect |
| 65. Dic24 | C2×C32 | semidirect |
| 85. C32×D3 | Q32 | direct (N × H) |
| 117. Q32 | C32×D3 | direct (N × H) |
| 119. C33 | C2×Q32 | semidirect |
| 140. C3×D3 | C3×Q32 | direct (N × H) |
| 161. C32 | D3×Q32 | direct (N × H) |
| 162. C32 | C2×C3×Q32 | semidirect |
| 174. D3 | C32×Q32 | direct (N × H) |
| 181. C3 | C3×D3×Q32 | direct (N × H) |
| 182. C3 | C2×C32×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D3×Q16 | 2 |
| C33×Q32 | 2 |
| C32×#829 | 2 |
| C32×Dic24 | 2 |
| C32×D3×C16 | 2 |
| C2×C32×Q32 | 3 |
| C3×D3×Q32 | 3 |