Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
356 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 99 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. C9×#948 | C2 | semidirect |
| 3. #11720858 | C2 | semidirect |
| 4. #11720585 | C2 | semidirect |
| 5. #11720291 | C2 | semidirect |
| 6. #11720285 | C2 | semidirect |
| 7. #11720275 | C2 | semidirect |
| 14. C3×#3675 | C4 | semidirect |
| 15. C3×#3674 | C4 | semidirect |
| 16. C3×#3673 | C4 | semidirect |
| 17. C3×#3672 | C4 | semidirect |
| 80. #3675 | Dic3 | semidirect |
| 81. #3674 | Dic3 | semidirect |
| 82. #3673 | Dic3 | semidirect |
| 83. #3672 | Dic3 | semidirect |
| 103. #948 | D9 | semidirect |
| 220. C3×C9 | #444 | semidirect |
| 310. C9 | #5197 | semidirect |
| 347. C3 | #10588825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63513 | 2 |
| C9×#948 | 2 |
| #11720858 | 2 |
| #11720585 | 2 |
| #11720291 | 2 |
| #11720285 | 2 |
| #11720275 | 2 |
| #10591674 | 3 |
| #10588825 | 3 |