Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
428 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×C3×#357 | C2 | semidirect |
| 3. C2×#4563 | C2 | semidirect |
| 4. C2×#4508 | C2 | semidirect |
| 5. #70646 | C2 | semidirect |
| 6. #70596 | C2 | semidirect |
| 7. #67807 | C2 | semidirect |
| 31. C2×#357 | D3 | semidirect |
| 72. #812 | D4 | semidirect |
| 359. C3 | #13387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83836 | 2 |
| C2×C3×#357 | 2 |
| C2×#4563 | 2 |
| C2×#4508 | 2 |
| #70646 | 2 |
| #70596 | 2 |
| #67807 | 2 |
| #13387 | 3 |