Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
520 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 520 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. #10709929 | C2 | semidirect |
| 2. #10709904 | C2 | semidirect |
| 4. #10709874 | C2 | semidirect |
| 5. #10709873 | C2 | semidirect |
| 6. #10681802 | C2 | semidirect |
| 7. C3×#12517 | C2 | semidirect |
| 24. #12517 | D3 | semidirect |
| 137. C3⋊C16 | SD32 | semidirect |
| 255. C3 | #123419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10709929 | 2 |
| #10709904 | 2 |
| #10709898 | 2 |
| #10709874 | 2 |
| #10709873 | 2 |
| #10681802 | 2 |
| C3×#12517 | 2 |
| #123419 | 3 |