Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
330 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. C2×C3×C9×C16 | C2 | semidirect |
| 3. #11720541 | C2 | semidirect |
| 10. #88525 | C4 | semidirect |
| 16. C2×C9×C16 | D3 | semidirect |
| 48. C2×C3×C16 | D9 | semidirect |
| 98. C2×C16 | C3⋊D9 | semidirect |
| 100. C3×C9 | #357 | semidirect |
| 144. C9 | #4509 | semidirect |
| 167. C3 | #10588186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| C2×C3×C9×C16 | 2 |
| #11720541 | 2 |
| #10589375 | 3 |
| #10588186 | 3 |