Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 107 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. C3×#63486 | C2 | semidirect |
| 3. C22×C9×C3⋊C8 | C2 | semidirect |
| 4. C2×#88416 | C2 | semidirect |
| 5. #11720284 | C2 | semidirect |
| 6. #11720278 | C2 | semidirect |
| 7. #11720276 | C2 | semidirect |
| 33. #63486 | D3 | semidirect |
| 53. C9×C3⋊C8 | D4 | semidirect |
| 89. C22×C3×C9 | SD16 | semidirect |
| 107. C22×C3⋊C8 | D9 | semidirect |
| 213. C22×C9 | #215 | semidirect |
| 238. C3×C9 | #465 | semidirect |
| 280. C3⋊C8 | #611 | semidirect |
| 317. C22×C3 | #3664 | semidirect |
| 348. C9 | #5048 | semidirect |
| 385. C22 | #88416 | semidirect |
| 394. C3 | #10588795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721819 | 2 |
| C3×#63486 | 2 |
| C22×C9×C3⋊C8 | 2 |
| C2×#88416 | 2 |
| #11720284 | 2 |
| #11720278 | 2 |
| #11720276 | 2 |
| #10591177 | 3 |
| #10588795 | 3 |