Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3332 conjugacy classes of subgroups; only the 687 normal subgroups are shown.
This group has 3332 conjugacy classes of subgroups — too many to draw. Only its 687 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. C2×C33×C4⋊C4 | C2 | semidirect |
| 3. C2×#88859 | C2 | semidirect |
| 4. C2×#88859 | C2 | semidirect |
| 5. #11722201 | C2 | semidirect |
| 18. C2×C32×C4⋊C4 | D3 | semidirect |
| 36. C2×C33×C4 | D4 | semidirect |
| 69. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 86. C2×C32×C4 | D12 | semidirect |
| 126. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 130. C33 | #394 | semidirect |
| 144. C2×C3×C4 | C4⋊(C3⋊D3) | semidirect |
| 182. C32 | #4991 | semidirect |
| 200. C2×C4 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 224. C3 | #10592690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C2×C33×C4⋊C4 | 2 |
| C2×#88859 | 2 |
| #11722201 | 2 |
| #10592690 | 3 |