Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
298 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 59 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×#4919 | C2 | semidirect |
| 2. C2×#4521 | C2 | semidirect |
| 3. C2×D96 | C2 | semidirect |
| 4. #69327 | C2 | semidirect |
| 5. C3×#1416 | C2 | semidirect |
| 6. (C2×D3)⋊C32 | C2 | semidirect |
| 7. #67577 | C2 | semidirect |
| 28. #1416 | D3 | semidirect |
| 41. C3×Q32 | D4 | semidirect |
| 50. D48 | D4 | semidirect |
| 105. Q32 | D12 | semidirect |
| 222. C3 | #13663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4919 | 2 |
| C2×#4521 | 2 |
| C2×D96 | 2 |
| #69327 | 2 |
| C3×#1416 | 2 |
| (C2×D3)⋊C32 | 2 |
| #67577 | 2 |
| #13663 | 3 |