Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1048 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1048 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 |
|---|---|---|
| 2. C3×#64078 | C2 | semidirect |
| 3. C2×#88800 | C2 | semidirect |
| 5. C32×#803 | C2 | semidirect |
| 22. #64078 | D3 | semidirect |
| 27. C3×#803 | D3 | semidirect |
| 79. #803 | C3⋊D3 | semidirect |
| 157. C33 | #497 | semidirect |
| 223. C32 | #4715 | semidirect |
| 224. C32 | #5086 | semidirect |
| 252. C3 | #10590374 | semidirect |
| 253. C3 | #10592414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723916 | 2 |
| C3×#64078 | 2 |
| C2×#88800 | 2 |
| C2×#88797 | 2 |
| C32×#803 | 2 |
| #10592414 | 3 |
| #10590374 | 3 |