Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 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. #71437 | C2 | semidirect |
| 4. #70665 | C2 | semidirect |
| 5. #70656 | C2 | semidirect |
| 6. C2×#4487 | C2 | semidirect |
| 7. C3×#1386 | C2 | semidirect |
| 34. #1386 | D3 | semidirect |
| 70. #812 | D4 | semidirect |
| 350. C3 | #13400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79120 | 2 |
| #71442 | 2 |
| #71437 | 2 |
| #70665 | 2 |
| #70656 | 2 |
| C2×#4487 | 2 |
| C3×#1386 | 2 |
| #13400 | 3 |