Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
758 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 113 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. C3×#3151 | C2 | semidirect |
| 2. #83302 | C2 | semidirect |
| 3. C2×#5073 | C2 | semidirect |
| 4. #71802 | C2 | semidirect |
| 5. #71759 | C2 | semidirect |
| 6. #69876 | C2 | semidirect |
| 7. #67667 | C2 | semidirect |
| 31. #3151 | D3 | semidirect |
| 138. C3×M16 | D8 | semidirect |
| 284. M16 | #213 | semidirect |
| 397. C3 | #10144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3151 | 2 |
| #83302 | 2 |
| C2×#5073 | 2 |
| #71802 | 2 |
| #71759 | 2 |
| #69876 | 2 |
| #67667 | 2 |
| #10144 | 3 |