Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 7. C4⋊(C3⋊#157) | C4 | semidirect |
| 8. C2×C33×C8 | C4 | semidirect |
| 9. C2×C3×C3⋊(C3⋊C8) | C4 | semidirect |
| 32. C2×C32×C8 | Dic3 | semidirect |
| 33. C2×C3⋊(C3⋊C8) | Dic3 | semidirect |
| 81. C2×C3×C8 | #157 | semidirect |
| 108. C33 | #340 | semidirect |
| 145. C2×C8 | C3⋊#157 | semidirect |
| 170. C32 | #4551 | semidirect |
| 205. C3 | #10590182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊#157) | 2 |
| C2×C3×C8×C3⋊D3 | 2 |
| #10590182 | 3 |
| #4551 | 9 |