Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1456 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1456 conjugacy classes of subgroups — too many to draw. Only its 403 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. C33×#131 | C2 | semidirect |
| 2. #11723992 | C2 | semidirect |
| 4. C2×#88851 | C2 | semidirect |
| 5. #11722194 | C2 | semidirect |
| 6. #11722193 | C2 | semidirect |
| 7. #11722189 | C2 | semidirect |
| 24. C32×#131 | D3 | semidirect |
| 71. C3×#131 | C3⋊D3 | semidirect |
| 125. #131 | C3⋊(C3⋊D3) | semidirect |
| 129. C33 | #471 | semidirect |
| 173. C32 | #5141 | semidirect |
| 202. C3 | #10592840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#131 | 2 |
| #11723992 | 2 |
| #11723990 | 2 |
| C2×#88851 | 2 |
| #11722194 | 2 |
| #11722193 | 2 |
| #11722189 | 2 |
| #10592840 | 3 |