Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
264 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 264 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. #10590168 | C3 | direct (N × H) |
| 14. C33×C8 | C8 | semidirect |
| 15. C3×C3⋊(C3⋊C8) | C8 | semidirect |
| 40. C32×C8 | C3×C8 | semidirect |
| 41. C3⋊(C3⋊C8) | C3×C8 | semidirect |
| 67. C33 | #322 | semidirect |
| 77. C3×C8 | #622 | semidirect |
| 102. C32 | C3×#322 | semidirect |
| 107. C8 | C3×#622 | semidirect |
| 120. C3 | #10590168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#622 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| #10590168 | 3 |
| C3×#322 | 9 |