Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. C3×#3414 | C2 | semidirect |
| 2. #83914 | C2 | semidirect |
| 3. #72076 | C2 | semidirect |
| 4. #71431 | C2 | semidirect |
| 5. #67818 | C2 | semidirect |
| 22. #3414 | D3 | semidirect |
| 33. C2×C3×Q16 | D4 | semidirect |
| 35. C2×C3×D8 | D4 | semidirect |
| 52. C2×C3×C16 | D4 | semidirect |
| 56. #817 | D4 | semidirect |
| 119. C2×Q16 | #67 | semidirect |
| 121. C2×D8 | #67 | semidirect |
| 140. C2×C16 | #67 | semidirect |
| 279. C3 | #13309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3414 | 2 |
| #83914 | 2 |
| #72076 | 2 |
| #71431 | 2 |
| #67818 | 2 |
| #13309 | 3 |