Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 91 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×#88543 | C2 | semidirect |
| 3. #11720961 | C2 | semidirect |
| 4. C2×D3×C9⋊C8 | C2 | semidirect |
| 5. C3×#63392 | C2 | semidirect |
| 6. #11720269 | C2 | semidirect |
| 7. #11720265 | C2 | semidirect |
| 35. #63392 | D3 | semidirect |
| 52. C3⋊(C9⋊C8) | D4 | semidirect |
| 92. C2×D3×C9 | SD16 | semidirect |
| 230. C3×C9 | #465 | semidirect |
| 315. C2×D3 | #3672 | semidirect |
| 333. C9 | #4778 | semidirect |
| 378. C3 | #10588717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88543 | 2 |
| C9×#938 | 2 |
| #11720961 | 2 |
| C2×D3×C9⋊C8 | 2 |
| C3×#63392 | 2 |
| #11720269 | 2 |
| #11720265 | 2 |
| #10591460 | 3 |
| #10588717 | 3 |