Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
658 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 103 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. #79312 | C2 | semidirect |
| 3. #73800 | C2 | semidirect |
| 4. #70756 | C2 | semidirect |
| 5. #70507 | C2 | semidirect |
| 6. #69469 | C2 | semidirect |
| 7. C3×#1303 | C2 | semidirect |
| 38. #1303 | D3 | semidirect |
| 129. C2×D12 | SD16 | semidirect |
| 425. C3 | #10240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79312 | 2 |
| #79055 | 2 |
| #73800 | 2 |
| #70756 | 2 |
| #70507 | 2 |
| #69469 | 2 |
| C3×#1303 | 2 |
| #10240 | 3 |