Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
230 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 99. C3×C4 | Q64 | semidirect |
| 119. C4 | #4522 | semidirect |
| 122. C3 | #13726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2247 | 2 |
| C2×#4522 | 2 |
| #69066 | 2 |
| C4×C3⋊C32 | 2 |
| #13726 | 3 |