Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
732 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 190 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. C3×#63656 | C2 | direct (N × H) |
| 5. C2×#63656 | C3 | direct (N × H) |
| 20. #63656 | C2×C3 | direct (N × H) |
| 94. C2×C33 | Q32 | semidirect |
| 134. C33 | C2×Q32 | semidirect |
| 161. C2×C32 | #829 | semidirect |
| 162. C2×C32 | C3×Q32 | semidirect |
| 188. C32 | C2×#829 | semidirect |
| 189. C32 | C2×C3×Q32 | semidirect |
| 201. C2×C3 | C3×#829 | semidirect |
| 202. C2×C3 | #63656 | direct (N × H) |
| 211. C3 | C2×C3×#829 | semidirect |
| 212. C3 | C2×#63656 | direct (N × H) |
| 213. C2 | C3×#63656 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| C2×C3×#3746 | 2 |
| C3×#63656 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| C2×#63656 | 3 |
| C2×C3×#829 | 3 |