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×C43 | C2 | semidirect |
| 4. C4×#208 | C2 | semidirect |
| 5. #4523 | C2 | semidirect |
| 14. C4×D12 | C4 | semidirect |
| 17. C4×Dic6 | C4 | semidirect |
| 18. #805 | C4 | direct (N × H) |
| 24. C43 | D3 | semidirect |
| 39. C3×C42 | C2×C4 | semidirect |
| 49. #208 | C2×C4 | semidirect |
| 80. D12 | C42 | semidirect |
| 84. Dic6 | C42 | semidirect |
| 108. C42 | C4×D3 | semidirect |
| 118. C3×C4 | #104 | semidirect |
| 158. C4 | #805 | 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×C43 | 2 |
| C2×#805 | 2 |
| C4×#208 | 2 |
| #4523 | 2 |
| C4×#104 | 3 |