Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4620 conjugacy classes of subgroups; only the 1155 normal subgroups are shown.
This group has 4620 conjugacy classes of subgroups — too many to draw. Only its 1155 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 |
|---|---|---|
| 4. C2×#88857 | C2 | semidirect |
| 5. C2×C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 6. #11723918 | C2 | direct (N × H) |
| 10. C22×C3⋊(C3⋊Dic3) | C4 | semidirect |
| 17. #88857 | C22 | semidirect |
| 18. C4×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 34. C2×C3⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 81. C2×C33 | #117 | semidirect |
| 111. C33 | C2×#117 | semidirect |
| 126. C2×C32 | #877 | semidirect |
| 150. C32 | C2×#877 | semidirect |
| 165. C2×C3 | #64086 | semidirect |
| 178. C3 | C2×#64086 | semidirect |
| 180. C2 | #11723918 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊(C3⋊Dic3) | 2 |
| C2×C33×C22⋊C4 | 2 |
| C2×#88864 | 2 |
| C2×#88857 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #11723918 | 2 |
| C2×#64086 | 3 |