Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
320 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 58 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×#63736 | C2 | semidirect |
| 4. #10593280 | C3 | direct (N × H) |
| 13. #63736 | C2×C3 | semidirect |
| 57. C3×C3⋊D3 | Q32 | semidirect |
| 83. C33 | C2×Q32 | semidirect |
| 102. C3⋊D3 | C3×Q32 | semidirect |
| 122. C32 | C2×C3×Q32 | semidirect |
| 140. C3 | #10593280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63802 | 2 |
| C3×#63764 | 2 |
| C3×#63736 | 2 |
| #10593280 | 3 |
| C2×C3×Q32 | 9 |