Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1960 conjugacy classes of subgroups; only the 461 normal subgroups are shown.
This group has 1960 conjugacy classes of subgroups — too many to draw. Only its 461 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. C2×#88852 | C2 | semidirect |
| 2. #11723915 | C2 | semidirect |
| 3. C4×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 4. C33×C4⋊C8 | C2 | semidirect |
| 5. #11722191 | C2 | semidirect |
| 20. C32×C4⋊C8 | D3 | semidirect |
| 33. C4⋊(C3⋊(C3⋊D3)) | D4 | semidirect |
| 55. C33×C4 | D8 | semidirect |
| 62. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 102. C32×C4 | D24 | semidirect |
| 109. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 111. C33 | #459 | semidirect |
| 149. C3×C4 | #3745 | semidirect |
| 153. C32 | #4843 | semidirect |
| 182. C4 | #88852 | semidirect |
| 185. C3 | #10592542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88852 | 2 |
| #11723915 | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C33×C4⋊C8 | 2 |
| #11722191 | 2 |
| #10592542 | 3 |