Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1004 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 306 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 |
|---|---|---|
| 6. C3×#5092 | C3 | direct (N × H) |
| 31. #5092 | C32 | direct (N × H) |
| 51. C33×C4 | Q16 | semidirect |
| 110. C32×C4 | #216 | semidirect |
| 111. C32×C4 | C3×Q16 | semidirect |
| 119. C33 | #494 | semidirect |
| 160. C3×C4 | C3×#216 | semidirect |
| 161. C3×C4 | C32×Q16 | semidirect |
| 166. C32 | #5092 | direct (N × H) |
| 167. C32 | C3×#494 | semidirect |
| 184. C4 | C32×#216 | semidirect |
| 187. C3 | C3×#5092 | direct (N × H) |
| 188. C3 | C32×#494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊Q8 | 2 |
| C2×C32×#216 | 2 |
| C32×#869 | 2 |
| C32×C4×C3⋊C8 | 2 |
| C32×#494 | 3 |
| C3×#5092 | 3 |