Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
380 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 23. #4496 | C4 | semidirect |
| 258. C3 | #12954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78573 | 2 |
| C3×#1953 | 2 |
| C2×#4496 | 2 |
| #70685 | 2 |
| #67735 | 2 |
| #67672 | 2 |
| #12954 | 3 |