Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
458 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. C2×#4513 | C2 | semidirect |
| 5. C2×#4487 | C2 | semidirect |
| 6. C3×#1383 | C2 | semidirect |
| 7. #67730 | C2 | semidirect |
| 23. (C2×D3)⋊C16 | C4 | semidirect |
| 31. #1383 | D3 | semidirect |
| 51. C2×C3×C16 | C2×C4 | semidirect |
| 63. C2×C3⋊C16 | C2×C4 | semidirect |
| 142. C2×C16 | C4×D3 | semidirect |
| 230. C2×D3 | #365 | semidirect |
| 289. C3 | #12929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#106 | 2 |
| #71431 | 2 |
| C2×#4513 | 2 |
| #70711 | 2 |
| C2×#4487 | 2 |
| C3×#1383 | 2 |
| #67730 | 2 |
| #12929 | 3 |