Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
698 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×#826 | C2 | semidirect |
| 2. C2×#4695 | C2 | semidirect |
| 3. C3×#1970 | C2 | semidirect |
| 4. C2×#4491 | C2 | semidirect |
| 5. #67657 | C2 | semidirect |
| 24. #1970 | D3 | semidirect |
| 32. C2×C3×D8 | D4 | semidirect |
| 55. C2×C3⋊C16 | D4 | semidirect |
| 125. C2×D8 | D12 | semidirect |
| 159. C2×C3×C4 | D16 | semidirect |
| 259. C2×C4 | #826 | semidirect |
| 297. C3 | #13325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#826 | 2 |
| C2×#4695 | 2 |
| C3×#1970 | 2 |
| C2×#4491 | 2 |
| #67657 | 2 |
| #13325 | 3 |