Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1876 conjugacy classes of subgroups; only the 353 normal subgroups are shown.
This group has 1876 conjugacy classes of subgroups — too many to draw. Only its 353 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. #11723979 | C2 | semidirect |
| 2. C2×#88860 | C2 | semidirect |
| 3. C2×C8×C3⋊(C3⋊D3) | C2 | semidirect |
| 4. #11723936 | C2 | semidirect |
| 5. C33×#102 | C2 | semidirect |
| 6. #11722191 | C2 | semidirect |
| 7. #11722177 | C2 | semidirect |
| 26. C32×#102 | D3 | semidirect |
| 45. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 69. C2×C3⋊(C3⋊D3) | D8 | semidirect |
| 79. C3×#102 | C3⋊D3 | semidirect |
| 140. #102 | C3⋊(C3⋊D3) | semidirect |
| 141. C33 | #466 | semidirect |
| 193. C32 | #4775 | semidirect |
| 232. C3 | #10592474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723979 | 2 |
| C2×#88860 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| #11723936 | 2 |
| C33×#102 | 2 |
| #11722191 | 2 |
| #11722177 | 2 |
| #10592474 | 3 |