Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1502 conjugacy classes of subgroups; only the 907 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 907 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. #69434 | C2 | semidirect |
| 10. C4×#208 | C4 | semidirect |
| 24. #803 | C2×C4 | semidirect |
| 25. C4×C3⋊C8 | C2×C4 | semidirect |
| 105. C3 | #20329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#376 | 2 |
| C2×C4×#208 | 2 |
| #69434 | 2 |
| #20329 | 3 |