Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
742 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#5027 | C2 | semidirect |
| 3. C3×#1984 | C2 | semidirect |
| 4. C2×#4485 | C2 | semidirect |
| 5. #67654 | C2 | semidirect |
| 22. #1984 | D3 | semidirect |
| 70. C2×C3×Q8 | D8 | semidirect |
| 93. C2×C3×C8 | SD16 | semidirect |
| 172. C2×Q8 | D24 | semidirect |
| 200. C2×C8 | #215 | semidirect |
| 284. C3 | #10262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5027 | 2 |
| C2×#4695 | 2 |
| C3×#1984 | 2 |
| C2×#4485 | 2 |
| #67654 | 2 |
| #10262 | 3 |