Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
246 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 63. C3×C16 | Q16 | semidirect |
| 105. C16 | Dic12 | semidirect |
| 135. C3 | #12524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69046 | 2 |
| #69044 | 2 |
| #68065 | 2 |
| #68064 | 2 |
| C3×#1311 | 2 |
| #12524 | 3 |