Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
150 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 38. C3×C32 | Q8 | semidirect |
| 39. C3⋊C32 | Q8 | semidirect |
| 77. C32 | Dic6 | semidirect |
| 135. C3 | #13734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69321 | 2 |
| #69320 | 2 |
| C3×#1423 | 2 |
| #67592 | 2 |
| #67589 | 2 |
| #67576 | 2 |
| #67575 | 2 |
| #13734 | 3 |