Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
812 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 258 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×#5081 | C3 | direct (N × H) |
| 35. C32×C3⋊C8 | Q8 | semidirect |
| 37. #5081 | C32 | direct (N × H) |
| 98. C3×C3⋊C8 | C3×Q8 | semidirect |
| 149. C33 | #501 | semidirect |
| 170. C3⋊C8 | C32×Q8 | semidirect |
| 209. C32 | #5081 | direct (N × H) |
| 210. C32 | C3×#501 | semidirect |
| 236. C3 | C3×#5081 | direct (N × H) |
| 237. C3 | C32×#501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊Q8 | 2 |
| C32×#870 | 2 |
| C32×#808 | 2 |
| C32×#807 | 2 |
| C32×#803 | 2 |
| C32×#501 | 3 |
| C3×#5081 | 3 |