Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
352 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 128 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×Dic36 | C3 | semidirect |
| 15. Dic36⋊C3 | C4 | direct (N × H) |
| 56. Dic36 | C3×C4 | semidirect |
| 59. C4×3−1+2 | Q16 | semidirect |
| 131. C4×C9 | C3×Q16 | semidirect |
| 141. 3−1+2 | C4×Q16 | semidirect |
| 193. C9 | C3×C4×Q16 | semidirect |
| 213. C4 | Dic36⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic36⋊C3 | 2 |
| C4×3−1+2⋊Q8 | 2 |
| C4×C8×3−1+2 | 2 |
| #63378⋊C3 | 2 |
| #63376⋊C3 | 2 |
| C3×C4×Dic12 | 3 |
| C4×Dic36 | 3 |