Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
3798 conjugacy classes of subgroups; only the 923 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 923 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×#383 | C2 | semidirect |
| 3. C2×#4937 | C2 | semidirect |
| 4. #74298 | C2 | direct (N × H) |
| 5. C2×#4665 | C2 | semidirect |
| 11. C2×#874 | C4 | semidirect |
| 13. C3×#383 | C22 | semidirect |
| 16. #4937 | C22 | semidirect |
| 17. #4665 | C22 | semidirect |
| 22. C2×#383 | D3 | semidirect |
| 29. C22×D12 | C2×C4 | semidirect |
| 33. C2×C3×C42 | C2×C4 | semidirect |
| 37. #874 | C2×C4 | semidirect |
| 48. #383 | C2×D3 | semidirect |
| 66. C2×D12 | C22×C4 | semidirect |
| 69. C3×C42 | C22×C4 | semidirect |
| 84. C2×C42 | C4×D3 | semidirect |
| 125. C42 | C2×C4×D3 | semidirect |
| 155. C2×C3 | #2380 | semidirect |
| 170. C3 | C2×#2380 | semidirect |
| 172. C2 | #74298 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#874 | 2 |
| C2×C3×#383 | 2 |
| C2×#4937 | 2 |
| #74298 | 2 |
| C2×#4665 | 2 |
| C2×#2380 | 3 |