Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#4517 | C2 | semidirect |
| 3. #71445 | C2 | semidirect |
| 6. #69794 | C2 | semidirect |
| 7. C3×#1376 | C2 | semidirect |
| 32. #1376 | D3 | semidirect |
| 313. C3 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4696 | 2 |
| C2×#4517 | 2 |
| #71445 | 2 |
| C2×#4516 | 2 |
| #71440 | 2 |
| #69794 | 2 |
| C3×#1376 | 2 |
| #13414 | 3 |