Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
658 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 658 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 |
|---|---|---|
| 1. #83314 | C2 | semidirect |
| 3. #73712 | C2 | semidirect |
| 4. C3×#1502 | C2 | semidirect |
| 5. #70774 | C2 | semidirect |
| 6. #70767 | C2 | semidirect |
| 7. #67620 | C2 | semidirect |
| 36. #1502 | D3 | semidirect |
| 144. C2×Dic6 | D8 | semidirect |
| 445. C3 | #10242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83314 | 2 |
| #83302 | 2 |
| #73712 | 2 |
| C3×#1502 | 2 |
| #70774 | 2 |
| #70767 | 2 |
| #67620 | 2 |
| #10242 | 3 |