Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
500 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
| 2. C3×#63502 | C2 | semidirect |
| 3. C2×C9×#213 | C2 | semidirect |
| 4. #11720964 | C2 | semidirect |
| 5. C2×#88421 | C2 | semidirect |
| 6. C2×#88415 | C2 | semidirect |
| 7. #11720274 | C2 | semidirect |
| 31. #63502 | D3 | semidirect |
| 53. C3⋊(C9⋊C8) | D4 | semidirect |
| 54. C9×C3⋊C8 | D4 | semidirect |
| 108. C2×#213 | D9 | semidirect |
| 226. C3×C9 | #496 | semidirect |
| 268. C3⋊C8 | #611 | semidirect |
| 325. C9 | #5074 | semidirect |
| 368. C3 | #10588834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88543 | 2 |
| C3×#63502 | 2 |
| C2×C9×#213 | 2 |
| #11720964 | 2 |
| C2×#88421 | 2 |
| C2×#88415 | 2 |
| #11720274 | 2 |
| #10591469 | 3 |
| #10588834 | 3 |