Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
620 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 155 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. #11721854 | C2 | semidirect |
| 5. C2×#88547 | C2 | semidirect |
| 7. #11720538 | C2 | semidirect |
| 30. C2×C9×Q16 | D3 | semidirect |
| 90. C2×C3×Q16 | D9 | semidirect |
| 185. C2×Q16 | C3⋊D9 | semidirect |
| 191. C3×C9 | #497 | semidirect |
| 262. C9 | #5190 | semidirect |
| 294. C3 | #10588870 | 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 |
| #11721854 | 2 |
| C2×#88548 | 2 |
| C2×#88547 | 2 |
| C2×#88524 | 2 |
| #11720538 | 2 |
| #10592889 | 3 |
| #10588870 | 3 |