Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
448 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 83 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×C8×C3⋊D9 | C2 | semidirect |
| 3. #11720936 | C2 | semidirect |
| 4. C2×#88423 | C2 | semidirect |
| 5. C9×#821 | C2 | semidirect |
| 6. C3×#63376 | C2 | semidirect |
| 7. #11720265 | C2 | semidirect |
| 36. #63376 | D3 | semidirect |
| 53. C3⋊(C9⋊C8) | D4 | semidirect |
| 89. C2×C3⋊D9 | SD16 | semidirect |
| 110. #821 | D9 | semidirect |
| 229. C3×C9 | #465 | semidirect |
| 331. C9 | #4807 | semidirect |
| 376. C3 | #10588458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D9 | 2 |
| #11721045 | 2 |
| #11720936 | 2 |
| C2×#88423 | 2 |
| C9×#821 | 2 |
| C3×#63376 | 2 |
| #11720265 | 2 |
| #10590841 | 3 |
| #10588458 | 3 |