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×#106 | C2 | semidirect |
| 4. C2×#817 | C2 | semidirect |
| 5. C2×#808 | C2 | semidirect |
| 6. D3×#106 | C2 | direct (N × H) |
| 15. C2×D3×C8 | C4 | semidirect |
| 19. C3×#106 | C22 | semidirect |
| 20. #817 | C22 | semidirect |
| 21. #808 | C22 | semidirect |
| 27. C2×#106 | 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. #106 | C2×D3 | direct (N × H) |
| 81. C3×C8 | C22×C4 | semidirect |
| 82. C3⋊C8 | C22×C4 | semidirect |
| 97. C2×C8 | C4×D3 | semidirect |
| 107. C2×D3 | #106 | direct (N × H) |
| 135. C8 | C2×C4×D3 | semidirect |
| 136. C2×C3 | C2×#106 | semidirect |
| 139. D3 | C2×#106 | direct (N × H) |
| 152. C3 | C22×#106 | semidirect |
| 154. C2 | D3×#106 | 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×#106 | 2 |
| C2×#817 | 2 |
| C2×#808 | 2 |
| D3×#106 | 2 |
| C22×#106 | 3 |