Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1168 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1168 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×#935 | C2 | semidirect |
| 3. C32×#886 | C2 | semidirect |
| 4. C33×#99 | C2 | semidirect |
| 5. C32×#806 | C2 | semidirect |
| 7. C3×#4742 | C3 | direct (N × H) |
| 11. C22×C32×Dic3 | C22 | semidirect |
| 15. C33×C22⋊C4 | C22 | semidirect |
| 17. C32×#217 | C22 | semidirect |
| 25. C3×#935 | C2×C3 | semidirect |
| 26. C3×#886 | C2×C3 | semidirect |
| 29. C32×#99 | D3 | semidirect |
| 30. C32×#99 | C2×C3 | semidirect |
| 31. C3×#806 | C2×C3 | semidirect |
| 51. #4742 | C32 | direct (N × H) |
| 63. C22×C3×Dic3 | C22×C3 | semidirect |
| 73. C32×C22⋊C4 | C2×D3 | semidirect |
| 74. C32×C22⋊C4 | C22×C3 | semidirect |
| 76. C3×#217 | C22×C3 | semidirect |
| 97. #935 | C2×C32 | semidirect |
| 98. #886 | C2×C32 | semidirect |
| 101. C3×#99 | C3×D3 | semidirect |
| 102. C3×#99 | C2×C32 | semidirect |
| 103. #806 | C2×C32 | semidirect |
| 162. C22×Dic3 | C22×C32 | semidirect |
| 172. C3×C22⋊C4 | C2×C3×D3 | semidirect |
| 173. C3×C22⋊C4 | C22×C32 | semidirect |
| 175. #217 | C22×C32 | semidirect |
| 216. #99 | C32×D3 | semidirect |
| 217. C33 | #458 | semidirect |
| 285. C22⋊C4 | C2×C32×D3 | semidirect |
| 320. C32 | #4742 | direct (N × H) |
| 321. C32 | C3×#458 | semidirect |
| 368. C3 | C3×#4742 | direct (N × H) |
| 369. C3 | C32×#458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1004 | 2 |
| C32×#935 | 2 |
| C32×#886 | 2 |
| C33×#99 | 2 |
| C32×#806 | 2 |
| C32×#458 | 3 |
| C3×#4742 | 3 |