Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2156 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 2156 conjugacy classes of subgroups — too many to draw. Only its 579 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×M16 | C2 | semidirect |
| 3. #11723967 | C2 | semidirect |
| 4. #11722195 | C2 | semidirect |
| 10. #89076 | C4 | semidirect |
| 12. C2×C4⋊(C3⋊(C3⋊D3)) | C4 | semidirect |
| 14. C2×#6308 | C4 | semidirect |
| 16. C33×M16 | C22 | semidirect |
| 20. C4×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 22. C2×C32×M16 | D3 | semidirect |
| 55. C32×M16 | C2×D3 | semidirect |
| 73. C2×C3×M16 | C3⋊D3 | semidirect |
| 111. C3×M16 | C2×C3⋊D3 | semidirect |
| 129. C2×M16 | C3⋊(C3⋊D3) | semidirect |
| 132. C33 | #421 | semidirect |
| 167. M16 | C2×C3⋊(C3⋊D3) | semidirect |
| 184. C32 | #5139 | semidirect |
| 221. C3 | #10592838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89076 | 2 |
| C2×C33×M16 | 2 |
| #11723967 | 2 |
| #11722195 | 2 |
| #10592838 | 3 |