Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1124 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 1124 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 |
|---|---|---|
| 1. C2×#88861 | C2 | semidirect |
| 3. C2×C32×#214 | C2 | semidirect |
| 4. #11723455 | C2 | semidirect |
| 5. C2×#88796 | C2 | semidirect |
| 6. C2×#88793 | C2 | semidirect |
| 7. C3⋊C8×C3⋊Dic3 | C2 | semidirect |
| 32. C2×C3×#214 | D3 | semidirect |
| 53. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 54. C32×C3⋊C8 | D4 | semidirect |
| 95. C3×C3⋊Dic3 | SD16 | semidirect |
| 107. C2×#214 | C3⋊D3 | semidirect |
| 153. C3×C3⋊C8 | #67 | semidirect |
| 212. C3⋊Dic3 | #214 | semidirect |
| 222. C33 | #492 | semidirect |
| 264. C3⋊C8 | #638 | semidirect |
| 316. C32 | #5076 | semidirect |
| 317. C32 | #5175 | semidirect |
| 357. C3 | #10591490 | semidirect |
| 358. C3 | #10592874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88861 | 2 |
| C3×#64149 | 2 |
| C2×C32×#214 | 2 |
| #11723455 | 2 |
| C2×#88796 | 2 |
| C2×#88793 | 2 |
| C3⋊C8×C3⋊Dic3 | 2 |
| #10592874 | 3 |
| #10591490 | 3 |