Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
560 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C2×C3×C9×Q16 | C2 | semidirect |
| 3. Q8×C3⋊Dic9 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 7. #11720537 | C2 | semidirect |
| 30. C2×C9×Q16 | D3 | semidirect |
| 91. C2×C3×Q16 | D9 | semidirect |
| 188. C2×Q16 | C3⋊D9 | semidirect |
| 195. C3×C9 | #464 | semidirect |
| 270. C9 | #5185 | semidirect |
| 305. C3 | #10588865 | 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 |
| #11721857 | 2 |
| Q8×C3⋊Dic9 | 2 |
| C2×#88548 | 2 |
| #11720582 | 2 |
| #11720543 | 2 |
| #11720537 | 2 |
| #10592884 | 3 |
| #10588865 | 3 |