Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #5757 | C2 | semidirect |
| 2. C2×C3×D16 | C2 | semidirect |
| 3. #5147 | C2 | semidirect |
| 4. #4912 | C2 | semidirect |
| 5. #4911 | C2 | semidirect |
| 6. D3×D16 | C2 | semidirect |
| 7. #4904 | C2 | semidirect |
| 8. #4901 | C2 | semidirect |
| 11. C2×C3×D8 | C22 | semidirect |
| 13. #912 | C22 | semidirect |
| 15. D3×D8 | C22 | semidirect |
| 16. #904 | C22 | semidirect |
| 18. C3×D16 | C22 | semidirect |
| 19. C3×D16 | C22 | semidirect |
| 20. C2×C3×C16 | C22 | semidirect |
| 21. #827 | C22 | semidirect |
| 22. #826 | C22 | semidirect |
| 23. #812 | C22 | semidirect |
| 24. Dic24 | C22 | semidirect |
| 25. #800 | C22 | semidirect |
| 26. D48 | C22 | semidirect |
| 27. #798 | C22 | semidirect |
| 28. D3×C16 | C22 | semidirect |
| 35. C2×D16 | D3 | semidirect |
| 65. C2×D8 | C2×D3 | semidirect |
| 72. D16 | C2×D3 | semidirect |
| 73. D16 | C2×D3 | semidirect |
| 77. C2×C16 | C2×D3 | semidirect |
| 163. C3 | #3415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5757 | 2 |
| C2×C3×D16 | 2 |
| #5147 | 2 |
| #4912 | 2 |
| #4911 | 2 |
| D3×D16 | 2 |
| #4904 | 2 |
| #4901 | 2 |
| #3415 | 3 |