Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1820 conjugacy classes of subgroups; only the 867 normal subgroups are shown.
This group has 1820 conjugacy classes of subgroups — too many to draw. Only its 867 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 |
|---|---|---|
| 4. #11722185 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 8. C33×M16 | C4 | semidirect |
| 13. C2×C3⋊(C3⋊(C3⋊C8)) | C4 | semidirect |
| 32. C32×M16 | Dic3 | semidirect |
| 66. C3×M16 | C3⋊Dic3 | semidirect |
| 86. C33 | #405 | semidirect |
| 100. M16 | C3⋊(C3⋊Dic3) | semidirect |
| 115. C32 | #5122 | semidirect |
| 135. C3 | #10592821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| #11723967 | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722185 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #10592821 | 3 |