Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
454 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 89 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×C3×#361 | C2 | semidirect |
| 3. C2×#4563 | C2 | semidirect |
| 4. #71448 | C2 | semidirect |
| 5. #70706 | C2 | semidirect |
| 6. #70687 | C2 | semidirect |
| 7. #67814 | C2 | semidirect |
| 31. C2×#361 | D3 | semidirect |
| 70. #819 | D4 | semidirect |
| 342. C3 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83830 | 2 |
| C2×C3×#361 | 2 |
| C2×#4563 | 2 |
| #71448 | 2 |
| #70706 | 2 |
| #70687 | 2 |
| #67814 | 2 |
| #13417 | 3 |