Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. C3×C4×D8 | C2 | semidirect |
| 3. C4×D24 | C2 | semidirect |
| 4. #4562 | C2 | semidirect |
| 5. #4491 | C2 | semidirect |
| 6. #4489 | C2 | semidirect |
| 7. C4×C3⋊C16 | C2 | semidirect |
| 16. #826 | C4 | direct (N × H) |
| 23. C4×D8 | D3 | semidirect |
| 33. C3×D8 | C2×C4 | semidirect |
| 42. D24 | C2×C4 | semidirect |
| 44. C3⋊C16 | C2×C4 | semidirect |
| 80. D8 | C4×D3 | semidirect |
| 99. C3×C4 | D16 | semidirect |
| 134. C4 | #826 | direct (N × H) |
| 137. C3 | C4×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D8 | 2 |
| C2×#826 | 2 |
| C4×D24 | 2 |
| #4562 | 2 |
| #4491 | 2 |
| #4489 | 2 |
| C4×C3⋊C16 | 2 |
| C4×D16 | 3 |