Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
558 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 6. #69340 | C2 | direct (N × H) |
| 36. C2×C3×C16 | Q8 | semidirect |
| 44. C2×C3⋊C16 | Q8 | semidirect |
| 79. C3×C16 | C2×Q8 | semidirect |
| 80. C3⋊C16 | C2×Q8 | semidirect |
| 92. C2×C16 | Dic6 | semidirect |
| 137. C16 | C2×Dic6 | semidirect |
| 163. C2×C3 | #2254 | semidirect |
| 175. C3 | C2×#2254 | semidirect |
| 176. C2 | #69340 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4874 | 2 |
| C2×C3×#367 | 2 |
| C2×#4505 | 2 |
| C2×Dic3×C16 | 2 |
| C2×#4490 | 2 |
| #69340 | 2 |
| C2×#2254 | 3 |