Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
535 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 535 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #73120 | C2 | direct (N × H) |
| 6. C2×#131⋊C3 | C4 | semidirect |
| 7. C2×#131⋊C3 | C4 | semidirect |
| 8. C2×#131⋊C3 | C4 | semidirect |
| 30. #131⋊C3 | C2×C4 | semidirect |
| 31. #131⋊C3 | C2×C4 | semidirect |
| 338. C2 | #73120 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#131⋊C3 | 2 |
| C2×#5423 | 2 |
| #73120 | 2 |
| C2×#1814 | 3 |
| C2×#819 | 4 |