Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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. #70853 | C2 | semidirect |
| 3. #69290 | C2 | semidirect |
| 4. #69044 | C2 | semidirect |
| 5. C3×D4⋊C16 | C2 | semidirect |
| 6. #67565 | C2 | semidirect |
| 7. #67504 | C2 | semidirect |
| 32. D4⋊C16 | D3 | semidirect |
| 249. C3 | #12399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79418 | 2 |
| #70853 | 2 |
| #69290 | 2 |
| #69044 | 2 |
| C3×D4⋊C16 | 2 |
| #67565 | 2 |
| #67504 | 2 |
| #12399 | 3 |