Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
750 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 4. #68064 | C2 | direct (N × H) |
| 130. C2×C3 | #1710 | semidirect |
| 141. C3 | C2×#1710 | semidirect |
| 142. C2 | #68064 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4681 | 2 |
| C2×#4682 | 2 |
| C2×C3×C82 | 2 |
| #68064 | 2 |
| C2×#1710 | 3 |