Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
844 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 844 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 |
|---|---|---|
| 2. C2×C3×#3746 | C2 | semidirect |
| 3. C3×#63654 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊(C3⋊C16) | C2 | semidirect |
| 5. C2×#63654 | C3 | direct (N × H) |
| 13. C3×#3746 | C22 | semidirect |
| 14. C3×C3⋊(C3⋊C16) | C22 | semidirect |
| 18. C2×#3746 | C2×C3 | semidirect |
| 20. #63654 | C2×C3 | direct (N × H) |
| 21. C2×C3⋊(C3⋊C16) | C2×C3 | semidirect |
| 50. #3746 | C22×C3 | semidirect |
| 53. C3⋊(C3⋊C16) | C22×C3 | semidirect |
| 96. C2×C33 | SD32 | semidirect |
| 139. C33 | C2×SD32 | semidirect |
| 169. C2×C32 | #827 | semidirect |
| 170. C2×C32 | C3×SD32 | semidirect |
| 199. C32 | C2×#827 | semidirect |
| 200. C32 | C2×C3×SD32 | semidirect |
| 215. C2×C3 | C3×#827 | semidirect |
| 216. C2×C3 | #63654 | direct (N × H) |
| 226. C3 | C2×C3×#827 | semidirect |
| 227. C3 | C2×#63654 | direct (N × H) |
| 229. C2 | C3×#63654 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| C2×C3×#3746 | 2 |
| C3×#63654 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| C2×#63654 | 3 |
| C2×C3×#827 | 3 |