Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1876 conjugacy classes of subgroups; only the 415 normal subgroups are shown.
This group has 1876 conjugacy classes of subgroups — too many to draw. Only its 415 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. #11723934 | C2 | semidirect |
| 3. C33×#107 | C2 | semidirect |
| 4. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 5. #11722179 | C2 | semidirect |
| 14. #88852 | C4 | semidirect |
| 17. C32×#107 | D3 | semidirect |
| 26. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 28. C33×C8 | C2×C4 | semidirect |
| 47. C3⋊(C3⋊Dic3) | D8 | semidirect |
| 50. C3×#107 | C3⋊D3 | semidirect |
| 61. C32×C8 | C4×D3 | semidirect |
| 87. #107 | C3⋊(C3⋊D3) | semidirect |
| 90. C33 | C4×D8 | semidirect |
| 99. C3×C8 | C4×C3⋊D3 | semidirect |
| 122. C32 | #4872 | semidirect |
| 132. C8 | C4×C3⋊(C3⋊D3) | semidirect |
| 146. C3 | #10592571 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88852 | 2 |
| #11723934 | 2 |
| C33×#107 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #11722179 | 2 |
| #10592571 | 3 |