Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3170 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 3170 conjugacy classes of subgroups — too many to draw. Only its 287 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. C2×C3×#3757 | C2 | semidirect |
| 3. C2×#88814 | C2 | semidirect |
| 9. C23×C3×C3⋊D3 | C4 | semidirect |
| 11. C22×C3×C3⋊Dic3 | C22 | semidirect |
| 17. C2×#3757 | D3 | semidirect |
| 45. C23×C3⋊D3 | Dic3 | semidirect |
| 56. C22×C3⋊Dic3 | C2×D3 | semidirect |
| 68. C22×C33 | C22⋊C4 | semidirect |
| 76. C2×C3×C3⋊D3 | C22⋊C4 | semidirect |
| 199. C22×C32 | (C2×D3)⋊C4 | semidirect |
| 200. C22×C32 | #217 | semidirect |
| 212. C2×C3⋊D3 | #217 | semidirect |
| 231. C33 | #379 | semidirect |
| 348. C22×C3 | (C2×D3)⋊Dic3 | semidirect |
| 349. C22×C3 | #3722 | semidirect |
| 375. C32 | #4955 | semidirect |
| 376. C32 | #5247 | semidirect |
| 422. C22 | #88814 | semidirect |
| 430. C3 | #10591706 | semidirect |
| 431. C3 | #10591714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C3⋊D3 | 2 |
| C2×C3×#3757 | 2 |
| C2×#88814 | 2 |
| #10591714 | 3 |
| #10591706 | 3 |