Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
732 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 282 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 |
|---|---|---|
| 7. C3×#4855 | C3 | direct (N × H) |
| 31. C33×C8 | Q8 | semidirect |
| 32. C32×C3⋊C8 | Q8 | semidirect |
| 34. #4855 | C32 | direct (N × H) |
| 82. C32×C8 | Dic6 | semidirect |
| 83. C32×C8 | C3×Q8 | semidirect |
| 84. C3×C3⋊C8 | C3×Q8 | semidirect |
| 125. C33 | #498 | semidirect |
| 140. C3×C8 | C3×Dic6 | semidirect |
| 141. C3×C8 | C32×Q8 | semidirect |
| 142. C3⋊C8 | C32×Q8 | semidirect |
| 173. C32 | #4855 | direct (N × H) |
| 174. C32 | C3×#498 | semidirect |
| 181. C8 | C32×Dic6 | semidirect |
| 195. C3 | C3×#4855 | direct (N × H) |
| 196. C3 | C32×#498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#888 | 2 |
| C33×#106 | 2 |
| C32×#817 | 2 |
| C32×C8×Dic3 | 2 |
| C32×#808 | 2 |
| C32×#498 | 3 |
| C3×#4855 | 3 |