Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
536 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 536 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 |
|---|---|---|
| 2. C4×#901 | C2 | semidirect |
| 3. C3×#1492 | C2 | semidirect |
| 4. #71797 | C2 | semidirect |
| 5. #70497 | C2 | semidirect |
| 6. #67710 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 37. #1492 | D3 | semidirect |
| 418. C3 | #9211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83299 | 2 |
| C4×#901 | 2 |
| C3×#1492 | 2 |
| #71797 | 2 |
| #70497 | 2 |
| #67710 | 2 |
| #67656 | 2 |
| #9211 | 3 |