Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 207 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. C2×C3×C8×C9 | C4 | semidirect |
| 10. C4×C3⋊Dic9 | C4 | semidirect |
| 32. C2×C8×C9 | Dic3 | semidirect |
| 69. C2×C3×C8 | Dic9 | semidirect |
| 93. C3×C9 | H(3,ℤ/4) | semidirect |
| 116. C2×C8 | C3⋊Dic9 | semidirect |
| 135. C9 | #4557 | semidirect |
| 156. C3 | #10588237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×M16 | 2 |
| #11721815 | 2 |
| #10589423 | 3 |
| #10588237 | 3 |