Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4788 conjugacy classes of subgroups; only the 899 normal subgroups are shown.
This group has 4788 conjugacy classes of subgroups — too many to draw. Only its 899 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. C22×C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. C2×C33×C4⋊C4 | C2 | semidirect |
| 4. C2×#88859 | C2 | semidirect |
| 5. C2×#88859 | C2 | semidirect |
| 6. C2×#88859 | C2 | semidirect |
| 7. C2×#88857 | C2 | semidirect |
| 8. #11723935 | C2 | direct (N × H) |
| 20. C2×C4×C3⋊(C3⋊D3) | C22 | semidirect |
| 21. C33×C4⋊C4 | C22 | semidirect |
| 22. #88859 | C22 | semidirect |
| 23. #88859 | C22 | semidirect |
| 24. #88859 | C22 | semidirect |
| 25. #88857 | C22 | semidirect |
| 28. C2×C32×C4⋊C4 | D3 | semidirect |
| 67. C32×C4⋊C4 | C2×D3 | semidirect |
| 91. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 119. C2×C33 | #123 | semidirect |
| 136. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 162. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 166. C33 | C2×#123 | semidirect |
| 188. C2×C32 | #894 | semidirect |
| 206. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 227. C32 | C2×#894 | semidirect |
| 249. C2×C3 | #64103 | semidirect |
| 272. C3 | C2×#64103 | semidirect |
| 275. C2 | #11723935 | direct (N × H) |
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 |
| C22×C4×C3⋊(C3⋊D3) | 2 |
| C2×C33×C4⋊C4 | 2 |
| C2×#88859 | 2 |
| C2×#88857 | 2 |
| #11723935 | 2 |
| C2×#64103 | 3 |