Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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. #5745 | C2 | semidirect |
| 3. C3×C4×M16 | C2 | semidirect |
| 4. #5125 | C2 | semidirect |
| 5. C2×#805 | C2 | semidirect |
| 6. #4717 | C2 | semidirect |
| 7. #4700 | C2 | semidirect |
| 14. #909 | C4 | semidirect |
| 15. #908 | C4 | semidirect |
| 19. #901 | C22 | semidirect |
| 20. C3×#97 | C22 | semidirect |
| 21. C3×C4×C8 | C22 | semidirect |
| 22. #819 | C22 | semidirect |
| 23. #805 | C22 | semidirect |
| 24. #805 | C22 | semidirect |
| 31. C4×M16 | D3 | semidirect |
| 52. Dic12 | C2×C4 | semidirect |
| 53. D24 | C2×C4 | semidirect |
| 54. #204 | C2×C4 | semidirect |
| 71. #97 | C2×D3 | semidirect |
| 72. C4×C8 | C2×D3 | semidirect |
| 166. C3 | #2956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5748 | 2 |
| #5745 | 2 |
| C3×C4×M16 | 2 |
| #5125 | 2 |
| C2×#805 | 2 |
| #4717 | 2 |
| #4700 | 2 |
| #2956 | 3 |