Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
378 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 114 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. #10593545 | C3 | direct (N × H) |
| 9. C3×C4×#157 | C4 | semidirect |
| 28. C4×#157 | C3×C4 | semidirect |
| 85. C33 | #382 | semidirect |
| 134. C32 | C3×#382 | semidirect |
| 164. C3 | #10593545 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊#157 | 2 |
| C2×C3×C4×#157 | 2 |
| C3×#63747 | 2 |
| #10593545 | 3 |
| C3×#382 | 9 |