Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
434 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 93 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. C9×#875 | C2 | semidirect |
| 2. C3×#63437 | C2 | semidirect |
| 3. C2×#88427 | C2 | semidirect |
| 4. C2×#88425 | C2 | semidirect |
| 5. C2×#88423 | C2 | semidirect |
| 7. C4×C3⋊(C9⋊C8) | C2 | semidirect |
| 35. #63437 | D3 | semidirect |
| 106. #875 | D9 | semidirect |
| 211. C3×C9 | #495 | semidirect |
| 297. C9 | #5059 | semidirect |
| 335. C3 | #10588740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#875 | 2 |
| C3×#63437 | 2 |
| C2×#88427 | 2 |
| C2×#88425 | 2 |
| C2×#88423 | 2 |
| C2×#88421 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| #10590353 | 3 |
| #10588740 | 3 |