Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1124 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 1124 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×#88861 | C2 | semidirect |
| 2. C2×C3×#3754 | C2 | semidirect |
| 4. #11723443 | C2 | semidirect |
| 5. C2×#88794 | C2 | semidirect |
| 6. C2×#88792 | C2 | semidirect |
| 7. Dic3×C3⋊(C3⋊C8) | C2 | semidirect |
| 29. C2×#3754 | D3 | semidirect |
| 53. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 54. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 96. C32×Dic3 | SD16 | semidirect |
| 152. C3⋊(C3⋊C8) | #67 | semidirect |
| 214. C3×Dic3 | #214 | semidirect |
| 222. C33 | #492 | semidirect |
| 314. Dic3 | #3754 | semidirect |
| 316. C32 | #5076 | semidirect |
| 317. C32 | #5175 | semidirect |
| 357. C3 | #10591490 | semidirect |
| 358. C3 | #10592775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88861 | 2 |
| C2×C3×#3754 | 2 |
| C32×#940 | 2 |
| #11723443 | 2 |
| C2×#88794 | 2 |
| C2×#88792 | 2 |
| Dic3×C3⋊(C3⋊C8) | 2 |
| #10592775 | 3 |
| #10591490 | 3 |