Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1092 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1092 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×#832 | C2 | semidirect |
| 4. C32×#803 | C2 | semidirect |
| 6. C3×#5071 | C3 | direct (N × H) |
| 17. C3×#870 | C2×C3 | semidirect |
| 20. C3×#832 | C2×C3 | semidirect |
| 21. C3×#803 | C2×C3 | semidirect |
| 30. #5071 | C32 | direct (N × H) |
| 56. #870 | C2×C32 | semidirect |
| 59. #832 | C2×C32 | semidirect |
| 60. #803 | C2×C32 | semidirect |
| 120. C33 | #490 | semidirect |
| 173. C32 | #5071 | direct (N × H) |
| 174. C32 | C3×#490 | semidirect |
| 198. C3 | C3×#5071 | direct (N × H) |
| 199. C3 | C32×#490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#127 | 2 |
| C32×#870 | 2 |
| C32×#832 | 2 |
| C32×#803 | 2 |
| C32×#490 | 3 |
| C3×#5071 | 3 |