Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4116 conjugacy classes of subgroups; only the 931 normal subgroups are shown.
This group has 4116 conjugacy classes of subgroups — too many to draw. Only its 931 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. C33×C4×Q8 | C2 | semidirect |
| 3. Q8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. #11723934 | C2 | semidirect |
| 5. C4⋊C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 6. C4×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 7. #11723913 | C2 | semidirect |
| 10. #89080 | C4 | semidirect |
| 23. C32×C4×Q8 | D3 | semidirect |
| 30. C33×Q8 | C2×C4 | semidirect |
| 37. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 39. C4×C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 65. C3×C4×Q8 | C3⋊D3 | semidirect |
| 72. C32×Q8 | C4×D3 | semidirect |
| 112. C4×Q8 | C3⋊(C3⋊D3) | semidirect |
| 117. C33 | #520 | semidirect |
| 119. C3×Q8 | C4×C3⋊D3 | semidirect |
| 156. C32 | #5574 | semidirect |
| 158. Q8 | C4×C3⋊(C3⋊D3) | semidirect |
| 182. C3 | #10596045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89080 | 2 |
| C33×C4×Q8 | 2 |
| Q8×C3⋊(C3⋊Dic3) | 2 |
| #11723934 | 2 |
| C4⋊C4×C3⋊(C3⋊D3) | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #11723913 | 2 |
| #10596045 | 3 |