Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
632 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 3. #10589414 | C3 | direct (N × H) |
| 102. C33 | #356 | semidirect |
| 150. C32 | #4548 | semidirect |
| 151. C32 | C3×#356 | semidirect |
| 171. C3 | C3×#4548 | semidirect |
| 172. C3 | #10589414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊Q8 | 2 |
| C3×#63663 | 2 |
| #10589414 | 3 |
| C3×#4548 | 3 |