Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4508 conjugacy classes of subgroups; only the 907 normal subgroups are shown.
This group has 4508 conjugacy classes of subgroups — too many to draw. Only its 907 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×#6308 | C2 | semidirect |
| 3. C2×C33×C4⋊C4 | C2 | semidirect |
| 6. C2×#88857 | C2 | semidirect |
| 7. C2×#88857 | C2 | semidirect |
| 8. #11723937 | C2 | direct (N × H) |
| 20. C2×#6308 | C22 | semidirect |
| 21. C33×C4⋊C4 | C22 | semidirect |
| 24. #88857 | C22 | semidirect |
| 25. #88857 | C22 | semidirect |
| 28. C2×C32×C4⋊C4 | D3 | semidirect |
| 37. C22×C3⋊(C3⋊D3) | Q8 | semidirect |
| 65. C32×C4⋊C4 | C2×D3 | semidirect |
| 77. C2×C3⋊(C3⋊D3) | C2×Q8 | semidirect |
| 86. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 112. C2×C33 | C22⋊Q8 | semidirect |
| 128. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 152. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 155. C33 | C2×C22⋊Q8 | semidirect |
| 175. C2×C32 | #896 | semidirect |
| 193. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 210. C32 | C2×#896 | semidirect |
| 230. C2×C3 | #64105 | semidirect |
| 249. C3 | C2×#64105 | semidirect |
| 251. C2 | #11723937 | 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×#6308 | 2 |
| C2×C33×C4⋊C4 | 2 |
| C2×#88859 | 2 |
| C2×#88857 | 2 |
| #11723937 | 2 |
| C2×#64105 | 3 |