Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 87 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. #71442 | C2 | semidirect |
| 3. C2×#4515 | C2 | semidirect |
| 4. #70718 | C2 | semidirect |
| 5. C2×#4497 | C2 | semidirect |
| 6. C2×#4493 | C2 | semidirect |
| 7. C3×#1385 | C2 | semidirect |
| 34. #1385 | D3 | semidirect |
| 342. C3 | #13392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79256 | 2 |
| #71442 | 2 |
| C2×#4515 | 2 |
| #70718 | 2 |
| C2×#4497 | 2 |
| C2×#4493 | 2 |
| C3×#1385 | 2 |
| #13392 | 3 |