Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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. D3×C9×Q16 | C2 | semidirect |
| 3. #11720568 | C2 | semidirect |
| 4. C3×#63387 | C2 | semidirect |
| 5. #11720245 | C2 | semidirect |
| 6. #11720242 | C2 | semidirect |
| 7. #11720237 | C2 | semidirect |
| 34. #63387 | D3 | semidirect |
| 82. D3×Q16 | D9 | semidirect |
| 174. C3×C9 | #510 | semidirect |
| 237. C9 | #4915 | semidirect |
| 264. C3 | #10588859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C9×Q16 | 2 |
| #11720811 | 2 |
| #11720568 | 2 |
| C3×#63387 | 2 |
| #11720245 | 2 |
| #11720242 | 2 |
| #11720237 | 2 |
| #10591045 | 3 |
| #10588859 | 3 |