Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1716 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 346 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. #10592929 | C3 | direct (N × H) |
| 25. C2×C3×C3⋊Dic3 | Q8 | semidirect |
| 68. C2×C3⋊Dic3 | C3×Q8 | semidirect |
| 108. C33 | #395 | semidirect |
| 160. C32 | #5230 | semidirect |
| 161. C32 | C3×#395 | semidirect |
| 186. C3 | C3×#5230 | semidirect |
| 187. C3 | #10592929 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| C2×C3×#3750 | 2 |
| C3×#63658 | 2 |
| #10592929 | 3 |
| C3×#5230 | 3 |