Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1276 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 1276 conjugacy classes of subgroups — too many to draw. Only its 182 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×#88860 | C2 | semidirect |
| 2. C2×C3×#3753 | C2 | semidirect |
| 3. C32×#940 | C2 | semidirect |
| 4. #11723517 | C2 | semidirect |
| 5. C2×#88790 | C2 | semidirect |
| 6. C2×#88789 | C2 | semidirect |
| 7. Dic3×C3⋊(C3⋊C8) | C2 | semidirect |
| 29. C2×#3753 | D3 | semidirect |
| 31. C3×#940 | D3 | semidirect |
| 54. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 55. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 99. C32×Dic3 | D8 | semidirect |
| 103. #940 | C3⋊D3 | semidirect |
| 157. C3⋊(C3⋊C8) | #67 | semidirect |
| 226. C3×Dic3 | #213 | semidirect |
| 234. C33 | #493 | semidirect |
| 338. Dic3 | #3753 | semidirect |
| 340. C32 | #5073 | semidirect |
| 341. C32 | #5151 | semidirect |
| 389. C3 | #10591482 | semidirect |
| 390. C3 | #10592772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88860 | 2 |
| C2×C3×#3753 | 2 |
| C32×#940 | 2 |
| #11723517 | 2 |
| C2×#88790 | 2 |
| C2×#88789 | 2 |
| Dic3×C3⋊(C3⋊C8) | 2 |
| #10592772 | 3 |
| #10591482 | 3 |