Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
988 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 166 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. C32×#870 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. #11722057 | C2 | semidirect |
| 5. #11722054 | C2 | semidirect |
| 25. C3×#870 | D3 | semidirect |
| 30. C4⋊(C3⋊(C3⋊C8)) | D3 | semidirect |
| 92. #870 | C3⋊D3 | semidirect |
| 205. C33 | #478 | semidirect |
| 293. C32 | #4847 | semidirect |
| 294. C32 | #5066 | semidirect |
| 331. C3 | #10590308 | semidirect |
| 332. C3 | #10592765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C32×#870 | 2 |
| C3×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #11722057 | 2 |
| #11722054 | 2 |
| #11722035 | 2 |
| #10592765 | 3 |
| #10590308 | 3 |