Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
11166 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 11166 conjugacy classes of subgroups — too many to draw. Only its 4427 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. C23×#216 | C2 | direct (N × H) |
| 13. C22×#216 | C22 | direct (N × H) |
| 28. C2×#216 | C23 | direct (N × H) |
| 39. C24×C3 | Q16 | semidirect |
| 49. #216 | C24 | direct (N × H) |
| 62. C23×C3 | C2×Q16 | semidirect |
| 73. C24 | #216 | direct (N × H) |
| 85. C22×C3 | C22×Q16 | semidirect |
| 91. C23 | C2×#216 | direct (N × H) |
| 102. C2×C3 | C23×Q16 | semidirect |
| 104. C22 | C22×#216 | direct (N × H) |
| 110. C3 | C24×Q16 | semidirect |
| 111. C2 | C23×#216 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×Q8 | 2 |
| C24×Dic6 | 2 |
| C23×#216 | 2 |
| C24×C3⋊C8 | 2 |
| C24×Q16 | 3 |