Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
836 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 254 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 |
|---|---|---|
| 3. #10589423 | C3 | direct (N × H) |
| 7. C2×C33×C8 | C4 | semidirect |
| 10. C3×C4×C3⋊Dic3 | C4 | semidirect |
| 32. C2×C32×C8 | Dic3 | semidirect |
| 33. C2×C32×C8 | C3×C4 | semidirect |
| 36. C4×C3⋊Dic3 | C3×C4 | semidirect |
| 83. C2×C3×C8 | C3×Dic3 | semidirect |
| 84. C2×C3×C8 | C3⋊Dic3 | semidirect |
| 113. C33 | H(3,ℤ/4) | semidirect |
| 145. C2×C8 | C3×C3⋊Dic3 | semidirect |
| 170. C32 | #4557 | semidirect |
| 171. C32 | C3×H(3,ℤ/4) | semidirect |
| 196. C3 | C3×#4557 | semidirect |
| 197. C3 | #10589423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| C3×#64135 | 2 |
| #10589423 | 3 |
| C3×#4557 | 3 |