Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
534 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 534 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 |
|---|---|---|
| 1. C2×C3×#472 | C2 | semidirect |
| 2. C2×#5147 | C2 | semidirect |
| 3. #83805 | C2 | semidirect |
| 4. C2×#4563 | C2 | semidirect |
| 5. #72007 | C2 | semidirect |
| 6. #70690 | C2 | semidirect |
| 7. #67734 | C2 | semidirect |
| 34. C2×#472 | D3 | semidirect |
| 411. C3 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#472 | 2 |
| C2×#5147 | 2 |
| #83805 | 2 |
| C2×#4563 | 2 |
| #72007 | 2 |
| #70690 | 2 |
| #67734 | 2 |
| #13323 | 3 |