Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1316 conjugacy classes of subgroups; only the 567 normal subgroups are shown.
This group has 1316 conjugacy classes of subgroups — too many to draw. Only its 567 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 |
|---|---|---|
| 6. C2×C33×C8 | C4 | semidirect |
| 9. C4×C3⋊(C3⋊Dic3) | C4 | semidirect |
| 22. C2×C32×C8 | Dic3 | semidirect |
| 48. C2×C3×C8 | C3⋊Dic3 | semidirect |
| 61. C33 | H(3,ℤ/4) | semidirect |
| 74. C2×C8 | C3⋊(C3⋊Dic3) | semidirect |
| 85. C32 | #4557 | semidirect |
| 103. C3 | #10589423 | 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 |
| #10589423 | 3 |