Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
202 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 54 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×#3771 | C2 | semidirect |
| 3. #10593264 | C3 | direct (N × H) |
| 10. C2×#3771 | C2×C3 | semidirect |
| 28. C2×C3×C3⋊D3 | C16 | semidirect |
| 63. C2×C3⋊D3 | C3×C16 | semidirect |
| 76. C33 | C22⋊C16 | semidirect |
| 124. C32 | C3×C22⋊C16 | semidirect |
| 152. C3 | #10593264 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3787 | 2 |
| C2×C3×#3771 | 2 |
| #10593264 | 3 |
| C3×C22⋊C16 | 9 |