Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. #79171 | C2 | semidirect |
| 5. #67822 | C2 | semidirect |
| 6. #67811 | C2 | semidirect |
| 7. #67727 | C2 | semidirect |
| 36. C2×C3×Q16 | Q8 | semidirect |
| 38. C2×C3×D8 | Q8 | semidirect |
| 129. C2×Q16 | Dic6 | semidirect |
| 131. C2×D8 | Dic6 | semidirect |
| 291. C3 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79171 | 2 |
| C3×#2145 | 2 |
| #72085 | 2 |
| #72076 | 2 |
| #67822 | 2 |
| #67811 | 2 |
| #67727 | 2 |
| #13373 | 3 |