Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
572 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 97 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×#5160 | C2 | semidirect |
| 2. C22×#826 | C2 | semidirect |
| 3. #79183 | C2 | semidirect |
| 4. C3×#2140 | C2 | semidirect |
| 5. C2×#4516 | C2 | semidirect |
| 6. C2×#4515 | C2 | semidirect |
| 7. #67724 | C2 | semidirect |
| 34. #2140 | D3 | semidirect |
| 45. C2×C3×D8 | D4 | semidirect |
| 78. #819 | D4 | semidirect |
| 81. C2×C3⋊C16 | D4 | semidirect |
| 178. C2×D8 | D12 | semidirect |
| 391. C3 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5160 | 2 |
| C22×#826 | 2 |
| #79183 | 2 |
| C3×#2140 | 2 |
| C2×#4516 | 2 |
| C2×#4515 | 2 |
| #67724 | 2 |
| #13319 | 3 |