Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3472 conjugacy classes of subgroups; only the 619 normal subgroups are shown.
This group has 3472 conjugacy classes of subgroups — too many to draw. Only its 619 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 |
|---|---|---|
| 1. #11724685 | C2 | semidirect |
| 2. C33×#135 | C2 | semidirect |
| 3. #11723992 | C2 | semidirect |
| 4. Q16×C3⋊(C3⋊D3) | C2 | semidirect |
| 5. #11723956 | C2 | semidirect |
| 6. #11723953 | C2 | semidirect |
| 7. C2×#88853 | C2 | semidirect |
| 8. #11723942 | C2 | semidirect |
| 30. C32×#135 | D3 | semidirect |
| 85. C3×#135 | C3⋊D3 | semidirect |
| 147. #135 | C3⋊(C3⋊D3) | semidirect |
| 151. C33 | #578 | semidirect |
| 202. C32 | #5771 | semidirect |
| 234. C3 | #10596242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724685 | 2 |
| C33×#135 | 2 |
| #11723992 | 2 |
| Q16×C3⋊(C3⋊D3) | 2 |
| #11723956 | 2 |
| #11723953 | 2 |
| C2×#88853 | 2 |
| #11723942 | 2 |
| #10596242 | 3 |