Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 3. #11720568 | C2 | direct (N × H) |
| 82. C2×C3×C9 | Q32 | semidirect |
| 114. C3×C9 | C2×Q32 | semidirect |
| 135. C2×C9 | #829 | semidirect |
| 156. C9 | C2×#829 | semidirect |
| 166. C2×C3 | #63388 | semidirect |
| 175. C3 | C2×#63388 | semidirect |
| 177. C2 | #11720568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| C2×#88521 | 2 |
| #11720568 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| C2×#63656 | 3 |
| C2×#63388 | 3 |