Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
369 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 3. #73037 | C2 | direct (N × H) |
| 88. C2×A4 | Q32 | semidirect |
| 133. A4 | C2×Q32 | semidirect |
| 140. C23 | Dic24 | semidirect |
| 173. C22 | C2×Dic24 | semidirect |
| 185. C2 | #73037 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5398 | 2 |
| C2×A4×C16 | 2 |
| #73037 | 2 |
| C2×#2216 | 3 |
| C2×Dic24 | 4 |