Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 9. C3×C9×Q16 | C4 | semidirect |
| 45. C9×Q16 | Dic3 | semidirect |
| 89. C3×Q16 | Dic9 | semidirect |
| 120. C3×C9 | #441 | semidirect |
| 142. Q16 | C3⋊Dic9 | semidirect |
| 162. C9 | #5184 | semidirect |
| 181. C3 | #10588864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| Q8×C3⋊Dic9 | 2 |
| #11720582 | 2 |
| #11720540 | 2 |
| #11720538 | 2 |
| #10592883 | 3 |
| #10588864 | 3 |