Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1084 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1084 conjugacy classes of subgroups — too many to draw. Only its 188 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. #11723916 | C2 | semidirect |
| 2. C3×#64084 | C2 | semidirect |
| 3. C2×#88800 | C2 | semidirect |
| 4. C2×#88797 | C2 | semidirect |
| 5. C2×#88796 | C2 | semidirect |
| 7. C32×C4×C3⋊C8 | C2 | semidirect |
| 30. #64084 | D3 | semidirect |
| 37. C3×C4×C3⋊C8 | D3 | semidirect |
| 110. C4×C3⋊C8 | C3⋊D3 | semidirect |
| 220. C33 | #495 | semidirect |
| 313. C32 | #4696 | semidirect |
| 314. C32 | #5059 | semidirect |
| 353. C3 | #10590370 | semidirect |
| 354. C3 | #10592395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723916 | 2 |
| C3×#64084 | 2 |
| C2×#88800 | 2 |
| C2×#88797 | 2 |
| C2×#88796 | 2 |
| C2×#88791 | 2 |
| C32×C4×C3⋊C8 | 2 |
| #10592395 | 3 |
| #10590370 | 3 |