Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
572 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 377 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 |
|---|---|---|
| 4. #5122 | C2 | semidirect |
| 5. Dic3×M16 | C2 | semidirect |
| 6. #5101 | C2 | semidirect |
| 7. C2×C8×Dic3 | C2 | semidirect |
| 10. C3×#131 | C4 | semidirect |
| 13. #948 | C4 | semidirect |
| 38. C3×M16 | C2×C4 | semidirect |
| 39. C2×C3×C8 | C2×C4 | semidirect |
| 47. #208 | C2×C4 | semidirect |
| 48. C2×C3⋊C8 | C2×C4 | semidirect |
| 53. #131 | Dic3 | direct (N × H) |
| 88. M16 | C2×Dic3 | semidirect |
| 92. C2×C8 | C2×Dic3 | semidirect |
| 107. Dic3 | #131 | direct (N × H) |
| 133. C3 | C4×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| Dic3×#41 | 2 |
| C2×#948 | 2 |
| #5122 | 2 |
| Dic3×M16 | 2 |
| #5101 | 2 |
| C2×C8×Dic3 | 2 |
| C4×#131 | 3 |