Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
578 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C22×C4×A4 | C2 | semidirect |
| 3. A4×C4⋊C4 | C2 | semidirect |
| 4. A4×C22⋊C4 | C2 | semidirect |
| 5. C42×A4 | C2 | semidirect |
| 6. C22×C4×D4 | C3 | semidirect |
| 8. D4×A4 | C4 | direct (N × H) |
| 16. C24×C4 | C2×C3 | semidirect |
| 23. C22×C4⋊C4 | C2×C3 | semidirect |
| 24. C22×C22⋊C4 | C2×C3 | semidirect |
| 25. C22×C42 | C2×C3 | semidirect |
| 28. C22×A4 | C2×C4 | semidirect |
| 34. C4×A4 | C2×C4 | semidirect |
| 35. C4×A4 | D4 | direct (N × H) |
| 44. C22×D4 | C3×C4 | semidirect |
| 65. C4×D4 | A4 | direct (N × H) |
| 95. C24 | C2×C3×C4 | semidirect |
| 133. C22×C4 | C2×C3×C4 | semidirect |
| 134. C22×C4 | C3×D4 | semidirect |
| 135. C22×C4 | C2×A4 | semidirect |
| 139. C4⋊C4 | C2×A4 | semidirect |
| 144. C22⋊C4 | C2×A4 | semidirect |
| 149. C42 | C2×A4 | semidirect |
| 154. A4 | C4×D4 | direct (N × H) |
| 188. D4 | C4×A4 | direct (N × H) |
| 245. C22 | C3×C4×D4 | semidirect |
| 246. C22 | C2×C4×A4 | semidirect |
| 254. C4 | C2×C4×A4 | semidirect |
| 255. C4 | D4×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×A4 | 2 |
| C22×C4×A4 | 2 |
| A4×C4⋊C4 | 2 |
| A4×C22⋊C4 | 2 |
| C42×A4 | 2 |
| C22×C4×D4 | 3 |
| C3×C4×D4 | 4 |