Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3612 conjugacy classes of subgroups; only the 1315 normal subgroups are shown.
This group has 3612 conjugacy classes of subgroups — too many to draw. Only its 1315 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 |
|---|---|---|
| 3. C2×C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. #11722201 | C2 | semidirect |
| 8. C22×C33×C4 | C4 | semidirect |
| 12. #88864 | C4 | direct (N × H) |
| 30. C2×C3⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 34. C22×C32×C4 | Dic3 | semidirect |
| 43. C22×C33 | C42 | semidirect |
| 49. C33×C4 | C22⋊C4 | semidirect |
| 76. C22×C3×C4 | C3⋊Dic3 | semidirect |
| 85. C22×C32 | C4×Dic3 | semidirect |
| 91. C32×C4 | #217 | semidirect |
| 97. C33 | C4×C22⋊C4 | semidirect |
| 119. C22×C4 | C3⋊(C3⋊Dic3) | semidirect |
| 127. C22×C3 | C4×C3⋊Dic3 | semidirect |
| 133. C3×C4 | #3757 | semidirect |
| 135. C32 | C4×#217 | semidirect |
| 157. C22 | C4×C3⋊(C3⋊Dic3) | semidirect |
| 164. C4 | #88864 | direct (N × H) |
| 165. C3 | C4×#3757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C33×C4 | 2 |
| C2×#88864 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #11722201 | 2 |
| C4×#3757 | 3 |