Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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×#1004 | C2 | semidirect |
| 2. C2×C3×#127 | C2 | semidirect |
| 3. C2×#932 | C2 | semidirect |
| 4. C2×#833 | C2 | semidirect |
| 5. #5077 | C2 | direct (N × H) |
| 6. C2×#805 | C2 | semidirect |
| 10. C22×C3×D4 | C22 | semidirect |
| 14. #1004 | C22 | semidirect |
| 19. C3×#127 | C22 | semidirect |
| 20. C2×C3×C42 | C22 | semidirect |
| 23. #932 | C22 | semidirect |
| 25. C2×#208 | C22 | semidirect |
| 26. #833 | C22 | semidirect |
| 27. #805 | C22 | semidirect |
| 30. C2×#127 | D3 | semidirect |
| 46. C2×C3×D4 | C23 | semidirect |
| 60. #235 | D4 | semidirect |
| 62. C2×D12 | D4 | semidirect |
| 64. C2×Dic6 | D4 | semidirect |
| 66. C3×C42 | C23 | semidirect |
| 70. #208 | C23 | semidirect |
| 81. C22×D4 | C2×D3 | semidirect |
| 88. #127 | C2×D3 | semidirect |
| 89. C2×C42 | C2×D3 | semidirect |
| 121. D12 | C2×D4 | semidirect |
| 125. Dic6 | C2×D4 | semidirect |
| 153. C2×D4 | C22×D3 | semidirect |
| 164. C42 | C22×D3 | semidirect |
| 223. C2×C3 | #453 | semidirect |
| 245. C3 | C2×#453 | semidirect |
| 251. C2 | #5077 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1004 | 2 |
| C2×C3×#127 | 2 |
| C2×#932 | 2 |
| C2×#833 | 2 |
| #5077 | 2 |
| C2×#805 | 2 |
| C2×#453 | 3 |