Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
436 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 115 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. #71801 | C2 | semidirect |
| 3. #71797 | C2 | semidirect |
| 4. C4×#819 | C2 | semidirect |
| 5. #69725 | C2 | semidirect |
| 263. C3 | #9726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3169 | 2 |
| #71801 | 2 |
| #71797 | 2 |
| C4×#819 | 2 |
| #69725 | 2 |
| #9726 | 3 |