Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. C3×C4×M16 | C2 | semidirect |
| 4. C42×Dic3 | C2 | semidirect |
| 5. #4555 | C2 | semidirect |
| 14. C4×D12 | C4 | semidirect |
| 17. C4×Dic6 | C4 | semidirect |
| 20. #825 | C4 | direct (N × H) |
| 23. C4×M16 | D3 | semidirect |
| 37. C3×M16 | C2×C4 | semidirect |
| 50. C4×Dic3 | C2×C4 | semidirect |
| 80. D12 | C42 | semidirect |
| 84. Dic6 | C42 | semidirect |
| 97. M16 | C4×D3 | semidirect |
| 117. C3×C4 | #104 | semidirect |
| 158. C4 | #825 | direct (N × H) |
| 162. C3 | C4×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#235 | 2 |
| C3×C4×M16 | 2 |
| C2×#825 | 2 |
| C42×Dic3 | 2 |
| #4555 | 2 |
| C4×#104 | 3 |