Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
272 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 272 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. #11720567 | C2 | semidirect |
| 4. C3×#63388 | C2 | semidirect |
| 5. #11720244 | C2 | semidirect |
| 6. #11720243 | C2 | semidirect |
| 7. #11720237 | C2 | semidirect |
| 31. #63388 | D3 | semidirect |
| 83. D3×Q16 | D9 | semidirect |
| 174. C3×C9 | #510 | semidirect |
| 238. C9 | #4918 | semidirect |
| 266. 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 |
| #11720812 | 2 |
| #11720567 | 2 |
| C3×#63388 | 2 |
| #11720244 | 2 |
| #11720243 | 2 |
| #11720237 | 2 |
| #10591047 | 3 |
| #10588859 | 3 |