Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1716 conjugacy classes of subgroups; only the 414 normal subgroups are shown.
This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 414 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 |
|---|---|---|
| 5. C3×#5230 | C3 | direct (N × H) |
| 25. C2×C32×Dic3 | Q8 | semidirect |
| 27. #5230 | C32 | direct (N × H) |
| 72. C2×C3×Dic3 | C3×Q8 | semidirect |
| 108. C33 | #395 | semidirect |
| 128. C2×Dic3 | C32×Q8 | semidirect |
| 160. C32 | #5230 | direct (N × H) |
| 161. C32 | C3×#395 | semidirect |
| 186. C3 | C3×#5230 | direct (N × H) |
| 187. C3 | C32×#395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| C2×C32×Dic3⋊C4 | 2 |
| C32×C3⋊#95 | 2 |
| C32×#395 | 3 |
| C3×#5230 | 3 |