Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
318 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 40. #817 | Q8 | semidirect |
| 44. C2×C3⋊C16 | Q8 | semidirect |
| 184. C3 | #13459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3162 | 2 |
| #70650 | 2 |
| #69844 | 2 |
| #67725 | 2 |
| #67663 | 2 |
| #13459 | 3 |