Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1652 conjugacy classes of subgroups; only the 477 normal subgroups are shown.
This group has 1652 conjugacy classes of subgroups — too many to draw. Only its 477 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. C33×C4⋊C8 | C2 | semidirect |
| 4. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 17. C32×C4⋊C8 | D3 | semidirect |
| 31. C4×C3⋊(C3⋊D3) | C8 | semidirect |
| 56. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 100. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 103. C33 | #431 | semidirect |
| 141. C32 | #4833 | semidirect |
| 170. C3 | #10592532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C3⋊(C3⋊D3) | 2 |
| C33×C4⋊C8 | 2 |
| #11722190 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592532 | 3 |