Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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. #78580 | C2 | semidirect |
| 3. C3×#1978 | C2 | semidirect |
| 4. C2×#4563 | C2 | semidirect |
| 5. #70687 | C2 | semidirect |
| 6. #67733 | C2 | semidirect |
| 7. #67672 | C2 | semidirect |
| 18. #5147 | C4 | semidirect |
| 33. #1978 | D3 | semidirect |
| 336. C3 | #13032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5147 | 2 |
| #78580 | 2 |
| C3×#1978 | 2 |
| C2×#4563 | 2 |
| #70687 | 2 |
| #67733 | 2 |
| #67672 | 2 |
| #13032 | 3 |