Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3444 conjugacy classes of subgroups; only the 891 normal subgroups are shown.
This group has 3444 conjugacy classes of subgroups — too many to draw. Only its 891 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. C2×C33×C4⋊C4 | C2 | semidirect |
| 5. C2×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 6. C2×#88857 | C2 | semidirect |
| 7. C2×C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 8. #11723939 | C2 | direct (N × H) |
| 17. C33×C4⋊C4 | C22 | semidirect |
| 21. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 22. #88857 | C22 | semidirect |
| 23. C4×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 24. C2×C32×C4⋊C4 | D3 | semidirect |
| 57. C32×C4⋊C4 | C2×D3 | semidirect |
| 78. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 104. C2×C33 | #126 | semidirect |
| 116. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 140. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 145. C33 | C2×#126 | semidirect |
| 163. C2×C32 | #898 | semidirect |
| 177. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 196. C32 | C2×#898 | semidirect |
| 214. C2×C3 | #64107 | semidirect |
| 233. C3 | C2×#64107 | semidirect |
| 235. C2 | #11723939 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C4⋊C4 | 2 |
| C2×#88859 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C2×#88857 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #11723939 | 2 |
| C2×#64107 | 3 |