Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
908 conjugacy classes of subgroups; only the 330 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 330 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 |
|---|---|---|
| 5. C3×#4699 | C3 | direct (N × H) |
| 24. #4699 | C32 | direct (N × H) |
| 38. C33×C4 | Q16 | semidirect |
| 82. C32×C4 | Dic12 | semidirect |
| 83. C32×C4 | C3×Q16 | semidirect |
| 90. C33 | #494 | semidirect |
| 121. C3×C4 | C3×Dic12 | semidirect |
| 122. C3×C4 | C32×Q16 | semidirect |
| 127. C32 | #4699 | direct (N × H) |
| 128. C32 | C3×#494 | semidirect |
| 142. C4 | C32×Dic12 | semidirect |
| 145. C3 | C3×#4699 | direct (N × H) |
| 146. C3 | C32×#494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Dic12 | 2 |
| C32×#869 | 2 |
| C33×C4×C8 | 2 |
| C32×#494 | 3 |
| C3×#4699 | 3 |