Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2548 conjugacy classes of subgroups; only the 691 normal subgroups are shown.
This group has 2548 conjugacy classes of subgroups — too many to draw. Only its 691 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 |
|---|---|---|
| 28. C2×C33×C4 | Q8 | semidirect |
| 34. C2×C3⋊(C3⋊Dic3) | Q8 | semidirect |
| 67. C2×C32×C4 | Dic6 | semidirect |
| 106. C33 | #395 | semidirect |
| 113. C2×C3×C4 | #634 | semidirect |
| 146. C32 | #4979 | semidirect |
| 160. C2×C4 | #6308 | semidirect |
| 177. C3 | #10592678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6308 | 2 |
| C2×C33×C4⋊C4 | 2 |
| C2×#88857 | 2 |
| #11722201 | 2 |
| #10592678 | 3 |