Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
7118 conjugacy classes of subgroups; only the 1459 normal subgroups are shown.
This group has 7118 conjugacy classes of subgroups — too many to draw. Only its 1459 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. C24×C3×Q8 | C2 | semidirect |
| 3. C2×#5231 | C2 | direct (N × H) |
| 4. C22×C3⋊#95 | C2 | semidirect |
| 8. C23×C3×Q8 | C22 | semidirect |
| 13. #5231 | C22 | direct (N × H) |
| 14. C2×C3⋊#95 | C22 | semidirect |
| 15. C24×Q8 | D3 | semidirect |
| 22. C24×D3 | Q8 | semidirect |
| 26. C22×C3×Q8 | C23 | semidirect |
| 35. C3⋊#95 | C23 | semidirect |
| 38. C23×Q8 | C2×D3 | semidirect |
| 54. C23×D3 | C2×Q8 | semidirect |
| 74. C22×Q8 | C22×D3 | semidirect |
| 97. C22×D3 | C22×Q8 | semidirect |
| 127. C22×C3 | #393 | semidirect |
| 161. C2×C3 | C2×#393 | semidirect |
| 170. C22 | #5231 | direct (N × H) |
| 179. C3 | C22×#393 | semidirect |
| 181. C2 | C2×#5231 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×Q8 | 2 |
| C23×(C2×D3)⋊C4 | 2 |
| C2×#5231 | 2 |
| C22×C3⋊#95 | 2 |
| C22×#393 | 3 |