Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
13310 conjugacy classes of subgroups; only the 8715 normal subgroups are shown.
This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 8715 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. C23×#208 | C2 | direct (N × H) |
| 3. C24×C3⋊C8 | C2 | semidirect |
| 10. C22×#208 | C22 | direct (N × H) |
| 11. C23×C3⋊C8 | C22 | semidirect |
| 23. C2×#208 | C23 | direct (N × H) |
| 24. C22×C3⋊C8 | C23 | semidirect |
| 33. C24×C3 | M16 | semidirect |
| 41. #208 | C24 | direct (N × H) |
| 42. C2×C3⋊C8 | C24 | semidirect |
| 54. C23×C3 | C2×M16 | semidirect |
| 62. C3⋊C8 | C25 | semidirect |
| 64. C24 | #208 | direct (N × H) |
| 75. C22×C3 | C22×M16 | semidirect |
| 82. C23 | C2×#208 | direct (N × H) |
| 92. C2×C3 | C23×M16 | semidirect |
| 95. C22 | C22×#208 | direct (N × H) |
| 101. C3 | C24×M16 | semidirect |
| 103. C2 | C23×#208 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C3×C4 | 2 |
| C23×#208 | 2 |
| C24×C3⋊C8 | 2 |
| C24×M16 | 3 |