Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2398 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 2398 conjugacy classes of subgroups — too many to draw. Only its 1067 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. C2×#4680 | C2 | direct (N × H) |
| 15. #4680 | C22 | direct (N × H) |
| 25. C22×C3×C8 | Q8 | semidirect |
| 56. C2×C3×C8 | C2×Q8 | semidirect |
| 68. C22×C8 | Dic6 | semidirect |
| 91. C3×C8 | C22×Q8 | semidirect |
| 102. C2×C8 | C2×Dic6 | semidirect |
| 109. C22×C3 | #498 | semidirect |
| 129. C8 | C22×Dic6 | semidirect |
| 130. C2×C3 | C2×#498 | semidirect |
| 133. C22 | #4680 | direct (N × H) |
| 141. C3 | C22×#498 | semidirect |
| 142. C2 | C2×#4680 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#869 | 2 |
| C22×C3×C4×C8 | 2 |
| C22×#817 | 2 |
| C2×#4680 | 2 |
| C22×#498 | 3 |