Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 109 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. #78491 | C2 | semidirect |
| 3. #70790 | C2 | semidirect |
| 4. #70774 | C2 | semidirect |
| 5. #69823 | C2 | semidirect |
| 6. C3×#1275 | C2 | semidirect |
| 7. #67738 | C2 | semidirect |
| 24. #4695 | C4 | semidirect |
| 25. #4694 | C4 | semidirect |
| 34. #1275 | D3 | semidirect |
| 129. C2×C3×C8 | D8 | semidirect |
| 273. C2×C8 | D24 | semidirect |
| 383. C3 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79303 | 2 |
| #78491 | 2 |
| #70790 | 2 |
| #70774 | 2 |
| #69823 | 2 |
| C3×#1275 | 2 |
| #67738 | 2 |
| #9293 | 3 |