Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3724 conjugacy classes of subgroups; only the 931 normal subgroups are shown.
This group has 3724 conjugacy classes of subgroups — too many to draw. Only its 931 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×Q8 | C2 | semidirect |
| 3. Q8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 5. #11723928 | C2 | semidirect |
| 7. C4×#6308 | C2 | semidirect |
| 10. Q8×C3⋊(C3⋊D3) | C4 | semidirect |
| 23. C32×C4×Q8 | D3 | semidirect |
| 64. C3×C4×Q8 | C3⋊D3 | semidirect |
| 112. C4×Q8 | C3⋊(C3⋊D3) | semidirect |
| 115. C33 | #519 | semidirect |
| 153. C32 | #5572 | semidirect |
| 178. C3 | #10596043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊(C3⋊D3) | 2 |
| C33×C4×Q8 | 2 |
| Q8×C3⋊(C3⋊Dic3) | 2 |
| #11723933 | 2 |
| #11723928 | 2 |
| #11723913 | 2 |
| C4×#6308 | 2 |
| #10596043 | 3 |