Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1512 conjugacy classes of subgroups; only the 461 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 461 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. #11723910 | C2 | semidirect |
| 3. C33×C4⋊C8 | C2 | semidirect |
| 5. #11722188 | C2 | semidirect |
| 18. C32×C4⋊C8 | D3 | semidirect |
| 28. C4⋊(C3⋊(C3⋊D3)) | Q8 | semidirect |
| 54. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 95. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 97. C33 | #474 | semidirect |
| 132. C32 | #4846 | semidirect |
| 158. C3 | #10592545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #11723910 | 2 |
| C33×C4⋊C8 | 2 |
| #11722191 | 2 |
| #11722188 | 2 |
| #10592545 | 3 |