Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
142 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 55 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. #4682 | C2 | semidirect |
| 3. C3×C4⋊C16 | C2 | semidirect |
| 5. #4504 | C2 | semidirect |
| 19. C4⋊C16 | D3 | semidirect |
| 32. D24 | Q8 | semidirect |
| 106. C3 | #2224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D24 | 2 |
| #4682 | 2 |
| C3×C4⋊C16 | 2 |
| #4509 | 2 |
| #4504 | 2 |
| #2224 | 3 |