Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#912 | C2 | semidirect |
| 2. C2×D3×D8 | C2 | semidirect |
| 3. C2×C3×D16 | C2 | semidirect |
| 4. C2×#827 | C2 | semidirect |
| 5. C2×#826 | C2 | semidirect |
| 6. #4911 | C2 | direct (N × H) |
| 7. C2×#800 | C2 | semidirect |
| 8. C2×#798 | C2 | semidirect |
| 13. C2×C3×D8 | C22 | semidirect |
| 17. #912 | C22 | semidirect |
| 19. D3×D8 | C22 | semidirect |
| 20. C2×Dic12 | C22 | semidirect |
| 23. C3×D16 | C22 | semidirect |
| 24. C2×C3×C16 | C22 | semidirect |
| 25. #827 | C22 | semidirect |
| 26. #826 | C22 | semidirect |
| 27. C2×C3⋊C16 | C22 | semidirect |
| 28. #800 | C22 | semidirect |
| 29. #798 | C22 | semidirect |
| 36. C2×D16 | D3 | semidirect |
| 54. C3×D8 | C23 | semidirect |
| 60. Dic12 | C23 | semidirect |
| 65. C3×C16 | C23 | semidirect |
| 66. C3⋊C16 | C23 | semidirect |
| 78. C2×D8 | C2×D3 | semidirect |
| 83. D16 | C2×D3 | semidirect |
| 86. C2×C16 | C2×D3 | semidirect |
| 134. D8 | C22×D3 | semidirect |
| 140. C16 | C22×D3 | semidirect |
| 182. C2×C3 | #509 | semidirect |
| 200. C3 | C2×#509 | semidirect |
| 205. C2 | #4911 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#912 | 2 |
| C2×D3×D8 | 2 |
| C2×C3×D16 | 2 |
| C2×#827 | 2 |
| C2×#826 | 2 |
| #4911 | 2 |
| C2×#800 | 2 |
| C2×#798 | 2 |
| C2×#509 | 3 |