Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
450 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×C3×C4×C16 | C2 | semidirect |
| 3. C2×#4508 | C2 | semidirect |
| 4. #69743 | C2 | semidirect |
| 21. C2×C4×C16 | D3 | semidirect |
| 38. C2×C3×C16 | D4 | semidirect |
| 102. C2×C16 | D12 | semidirect |
| 161. C3×C4 | #350 | semidirect |
| 198. C4 | #4508 | semidirect |
| 202. C3 | #13191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78458 | 2 |
| C2×C3×C4×C16 | 2 |
| C2×#4508 | 2 |
| #69743 | 2 |
| #13191 | 3 |