Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
238 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #70881 | C2 | semidirect |
| 3. #67763 | C2 | semidirect |
| 4. #67500 | C2 | semidirect |
| 5. C16×C3⋊C8 | C2 | semidirect |
| 61. C3×C16 | M16 | semidirect |
| 92. C3⋊C8 | D16 | semidirect |
| 109. C16 | #208 | semidirect |
| 150. C3 | #12081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D16 | 2 |
| #70881 | 2 |
| #67763 | 2 |
| #67500 | 2 |
| C16×C3⋊C8 | 2 |
| #12081 | 3 |