Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
826 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 242 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. C3×#63747 | C2 | direct (N × H) |
| 3. C2×#63747 | C3 | direct (N × H) |
| 6. C22×C3×#157 | C4 | semidirect |
| 9. #63747 | C2×C3 | direct (N × H) |
| 17. C2×C3×#157 | C2×C4 | semidirect |
| 22. C22×#157 | C3×C4 | semidirect |
| 47. C2×#157 | C2×C3×C4 | semidirect |
| 49. C2×C33 | #95 | semidirect |
| 51. C3×C3⋊D3 | #95 | semidirect |
| 78. C33 | C2×#95 | semidirect |
| 97. C2×C32 | C3×#95 | semidirect |
| 99. C3⋊D3 | C3×#95 | semidirect |
| 128. C32 | C2×C3×#95 | semidirect |
| 144. C2×C3 | #63747 | direct (N × H) |
| 159. C3 | C2×#63747 | direct (N × H) |
| 163. C2 | C3×#63747 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×#157 | 2 |
| C3×#63747 | 2 |
| C2×#63747 | 3 |
| C2×C3×#95 | 9 |