Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1680 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 1680 conjugacy classes of subgroups — too many to draw. Only its 515 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. #11723910 | C2 | semidirect |
| 4. #11722180 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 51. C33×C4 | SD16 | semidirect |
| 93. C32×C4 | #214 | semidirect |
| 102. C33 | #461 | semidirect |
| 135. C3×C4 | #3754 | semidirect |
| 139. C32 | #5019 | semidirect |
| 163. C4 | #88861 | semidirect |
| 166. C3 | #10592718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×D4 | 2 |
| C2×#88861 | 2 |
| #11723910 | 2 |
| #11722180 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592718 | 3 |