Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 107 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. C3×C4×#108 | C2 | semidirect |
| 3. #69859 | C2 | semidirect |
| 4. #69853 | C2 | semidirect |
| 5. C8×#208 | C2 | semidirect |
| 26. C4×#108 | D3 | semidirect |
| 263. C3 | #9724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78470 | 2 |
| C3×C4×#108 | 2 |
| #69859 | 2 |
| #69853 | 2 |
| C8×#208 | 2 |
| #9724 | 3 |