Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
388 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 186 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 |
|---|---|---|
| 4. C3×#4505 | C3 | direct (N × H) |
| 7. C33×C16 | C4 | semidirect |
| 18. #4505 | C32 | direct (N × H) |
| 25. C32×C16 | Dic3 | semidirect |
| 26. C32×C16 | C3×C4 | semidirect |
| 56. C3×C16 | C3×Dic3 | semidirect |
| 57. C3×C16 | C32×C4 | semidirect |
| 71. C33 | #367 | semidirect |
| 91. C16 | C32×Dic3 | semidirect |
| 104. C32 | #4505 | direct (N × H) |
| 105. C32 | C3×#367 | semidirect |
| 121. C3 | C3×#4505 | direct (N × H) |
| 122. C3 | C32×#367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C16 | 2 |
| C32×#818 | 2 |
| C32×#367 | 3 |
| C3×#4505 | 3 |