Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
752 conjugacy classes of subgroups; only the 358 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 358 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×#63639 | C2 | semidirect |
| 3. C2×C3×C3⋊(C3⋊C16) | C2 | semidirect |
| 4. #10592839 | C3 | direct (N × H) |
| 14. #63639 | C2×C3 | semidirect |
| 15. C2×C3⋊(C3⋊C16) | C2×C3 | semidirect |
| 91. C33 | #504 | semidirect |
| 128. C32 | #5140 | semidirect |
| 129. C32 | C3×#504 | semidirect |
| 145. C3 | C3×#5140 | semidirect |
| 146. C3 | #10592839 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#131 | 2 |
| C3×#63639 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| #10592839 | 3 |
| C3×#5140 | 3 |