Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. C2×C3×#107 | C2 | semidirect |
| 4. C2×#818 | C2 | semidirect |
| 5. C2×#807 | C2 | semidirect |
| 6. D3×#107 | C2 | direct (N × H) |
| 15. C2×D3×C8 | C4 | semidirect |
| 19. C3×#107 | C22 | semidirect |
| 20. #818 | C22 | semidirect |
| 21. #807 | C22 | semidirect |
| 27. C2×#107 | D3 | direct (N × H) |
| 39. C2×C3×C8 | C2×C4 | semidirect |
| 46. C2×C3⋊C8 | C2×C4 | semidirect |
| 48. D3×C8 | C2×C4 | semidirect |
| 62. #107 | C2×D3 | direct (N × H) |
| 82. C3×C8 | C22×C4 | semidirect |
| 83. C3⋊C8 | C22×C4 | semidirect |
| 98. C2×C8 | C4×D3 | semidirect |
| 109. C2×D3 | #107 | direct (N × H) |
| 139. C8 | C2×C4×D3 | semidirect |
| 140. C2×C3 | C2×#107 | semidirect |
| 144. D3 | C2×#107 | direct (N × H) |
| 159. C3 | C22×#107 | semidirect |
| 161. C2 | D3×#107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C2×C3×#107 | 2 |
| C2×#818 | 2 |
| C2×#807 | 2 |
| D3×#107 | 2 |
| C22×#107 | 3 |