Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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. #4512 | C2 | direct (N × H) |
| 9. C3×M32 | C4 | semidirect |
| 11. C2×C3×C16 | C4 | semidirect |
| 14. #812 | C4 | semidirect |
| 16. C2×C3⋊C16 | C4 | semidirect |
| 34. C3×C16 | C2×C4 | semidirect |
| 35. C3⋊C16 | C2×C4 | semidirect |
| 41. M32 | Dic3 | semidirect |
| 44. C2×C16 | Dic3 | semidirect |
| 75. C16 | C2×Dic3 | semidirect |
| 101. C2×C3 | #347 | semidirect |
| 112. C3 | C2×#347 | semidirect |
| 115. C2 | #4512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×M32 | 2 |
| C2×#815 | 2 |
| C2×#812 | 2 |
| #4512 | 2 |
| C2×#347 | 3 |