Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1820 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1820 conjugacy classes of subgroups — too many to draw. Only its 407 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 |
|---|---|---|
| 2. #11723977 | C2 | semidirect |
| 3. C2×#88861 | C2 | semidirect |
| 4. C2×#88853 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 88. C33 | #495 | semidirect |
| 118. C32 | #5155 | semidirect |
| 139. C3 | #10592854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| #11723977 | 2 |
| C2×#88861 | 2 |
| C2×#88853 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #10592854 | 3 |