Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
512 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #73618 | C2 | semidirect |
| 5. #70770 | C2 | semidirect |
| 6. #67736 | C2 | semidirect |
| 7. #67620 | C2 | semidirect |
| 15. #5094 | C4 | semidirect |
| 16. #5075 | C4 | semidirect |
| 147. C4×Dic3 | SD16 | semidirect |
| 384. C3 | #9238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83315 | 2 |
| #73618 | 2 |
| C3×#1502 | 2 |
| #71815 | 2 |
| #70770 | 2 |
| #67736 | 2 |
| #67620 | 2 |
| #9238 | 3 |