Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
542 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 542 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 |
|---|---|---|
| 2. C3×#1997 | C2 | semidirect |
| 3. #71774 | C2 | semidirect |
| 5. #70490 | C2 | semidirect |
| 7. M16×C3⋊C8 | C2 | semidirect |
| 28. #1997 | D3 | semidirect |
| 107. C3×M16 | SD16 | semidirect |
| 192. C3⋊C8 | #100 | semidirect |
| 216. M16 | #215 | semidirect |
| 301. C3 | #9793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5085 | 2 |
| C3×#1997 | 2 |
| #71774 | 2 |
| #70502 | 2 |
| #70490 | 2 |
| #69876 | 2 |
| M16×C3⋊C8 | 2 |
| #9793 | 3 |