Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
566 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 125 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. #10709904 | C2 | semidirect |
| 2. #10709898 | C2 | semidirect |
| 3. #10709898 | C2 | semidirect |
| 4. #10709873 | C2 | semidirect |
| 5. #10709872 | C2 | semidirect |
| 6. #10681802 | C2 | semidirect |
| 7. C3×#12515 | C2 | semidirect |
| 25. #12515 | D3 | semidirect |
| 140. C3⋊C16 | D16 | semidirect |
| 270. C3 | #123412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10709904 | 2 |
| #10709898 | 2 |
| #10709873 | 2 |
| #10709872 | 2 |
| #10681802 | 2 |
| C3×#12515 | 2 |
| #123412 | 3 |