Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
878 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 331 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. #68065 | C2 | direct (N × H) |
| 52. C2×C3×C8 | Q16 | semidirect |
| 88. C3×C8 | C2×Q16 | semidirect |
| 97. C2×C8 | Dic12 | semidirect |
| 125. C8 | C2×Dic12 | semidirect |
| 126. C2×C3 | #1713 | semidirect |
| 137. C3 | C2×#1713 | semidirect |
| 138. C2 | #68065 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4699 | 2 |
| C2×#4682 | 2 |
| C2×C3×C82 | 2 |
| #68065 | 2 |
| C2×#1713 | 3 |