Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 49. C3×C4×C9 | Q16 | semidirect |
| 108. C4×C9 | #216 | semidirect |
| 115. C3×C9 | #494 | semidirect |
| 153. C3×C4 | #3674 | semidirect |
| 161. C9 | #5092 | semidirect |
| 178. C4 | #88427 | semidirect |
| 181. C3 | #10588765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#869 | 2 |
| C3×#63431 | 2 |
| C2×#88427 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| #10590387 | 3 |
| #10588765 | 3 |