Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×C3×D16 | C2 | semidirect |
| 2. #5151 | C2 | semidirect |
| 3. C2×#826 | C2 | semidirect |
| 4. C2×D48 | C2 | semidirect |
| 5. Dic3×C16 | C2 | semidirect |
| 19. C2×D16 | D3 | semidirect |
| 33. C3×C16 | D4 | semidirect |
| 34. C3⋊C16 | D4 | semidirect |
| 69. C16 | #67 | semidirect |
| 77. Dic3 | D16 | semidirect |
| 102. C3 | #2246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D16 | 2 |
| #5151 | 2 |
| C2×#826 | 2 |
| C2×D48 | 2 |
| Dic3×C16 | 2 |
| #2246 | 3 |