Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1168 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1168 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×#64083 | C2 | semidirect |
| 3. C2×#88796 | C2 | semidirect |
| 4. C2×#88791 | C2 | semidirect |
| 5. C32×#803 | C2 | semidirect |
| 22. #64083 | D3 | semidirect |
| 27. C3×#803 | D3 | semidirect |
| 38. C32×C3⋊C8 | D4 | semidirect |
| 81. #803 | C3⋊D3 | semidirect |
| 109. C3×C3⋊C8 | D12 | semidirect |
| 164. C33 | #496 | semidirect |
| 192. C3⋊C8 | C4⋊(C3⋊D3) | semidirect |
| 236. C32 | #4712 | semidirect |
| 237. C32 | #5074 | semidirect |
| 269. C3 | #10590371 | semidirect |
| 270. C3 | #10592411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723916 | 2 |
| C3×#64083 | 2 |
| C2×#88796 | 2 |
| C2×#88791 | 2 |
| C32×#803 | 2 |
| #10592411 | 3 |
| #10590371 | 3 |