Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1652 conjugacy classes of subgroups; only the 851 normal subgroups are shown.
This group has 1652 conjugacy classes of subgroups — too many to draw. Only its 851 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 |
|---|---|---|
| 4. #11722188 | C2 | semidirect |
| 5. #11722187 | C2 | semidirect |
| 9. C33×M16 | C4 | semidirect |
| 31. C33×C8 | C2×C4 | semidirect |
| 35. C32×M16 | Dic3 | semidirect |
| 67. C32×C8 | C2×Dic3 | semidirect |
| 75. C3×M16 | C3⋊Dic3 | semidirect |
| 98. C33 | #428 | semidirect |
| 108. C3×C8 | C2×C3⋊Dic3 | semidirect |
| 115. M16 | C3⋊(C3⋊Dic3) | semidirect |
| 133. C32 | #5121 | semidirect |
| 143. C8 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 158. C3 | #10592820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| #11723967 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #11722188 | 2 |
| #11722187 | 2 |
| #10592820 | 3 |