Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
248 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10590174 | C3 | direct (N × H) |
| 7. C3×#3708 | C4 | semidirect |
| 23. #3708 | C3×C4 | semidirect |
| 27. C3×C3⋊Dic3 | C16 | semidirect |
| 61. C3⋊Dic3 | C3×C16 | semidirect |
| 65. C33 | C4×C16 | semidirect |
| 99. C32 | C3×C4×C16 | semidirect |
| 116. C3 | #10590174 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3708 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| #10590174 | 3 |
| C3×C4×C16 | 9 |