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 |
|---|---|---|
| 2. C4×D24 | C2 | semidirect |
| 3. C3×C4×C16 | C2 | semidirect |
| 4. #4509 | C2 | semidirect |
| 5. #4504 | C2 | semidirect |
| 14. D48 | C4 | direct (N × H) |
| 19. C4×C16 | D3 | semidirect |
| 28. D24 | C2×C4 | semidirect |
| 30. C3×C16 | C2×C4 | semidirect |
| 60. C16 | C4×D3 | semidirect |
| 66. C3×C4 | D16 | semidirect |
| 91. C4 | D48 | direct (N × H) |
| 94. C3 | C4×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D48 | 2 |
| C4×D24 | 2 |
| C3×C4×C16 | 2 |
| #4509 | 2 |
| #4504 | 2 |
| C4×D16 | 3 |