Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
130 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 50 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. #10590082 | C3 | direct (N × H) |
| 24. C3×#157 | C16 | semidirect |
| 51. #157 | C3×C16 | semidirect |
| 59. C33 | C4⋊C16 | semidirect |
| 92. C32 | C3×C4⋊C16 | semidirect |
| 113. C3 | #10590082 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×#157 | 2 |
| C3×#63764 | 2 |
| #10590082 | 3 |
| C3×C4⋊C16 | 9 |