Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
162 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 67 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. Dic3×Q16 | C2 | semidirect |
| 4. #4564 | C2 | semidirect |
| 6. #4505 | C2 | semidirect |
| 7. Dic3×C16 | C2 | semidirect |
| 13. C3×SD32 | C4 | semidirect |
| 32. C3×Q16 | C2×C4 | semidirect |
| 43. C3×C16 | C2×C4 | semidirect |
| 49. SD32 | Dic3 | direct (N × H) |
| 76. Q16 | C2×Dic3 | semidirect |
| 88. C16 | C2×Dic3 | semidirect |
| 99. Dic3 | SD32 | direct (N × H) |
| 130. C3 | C4×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×SD32 | 2 |
| Dic3×Q16 | 2 |
| Dic3×D8 | 2 |
| #4564 | 2 |
| #4562 | 2 |
| #4505 | 2 |
| Dic3×C16 | 2 |
| C4×SD32 | 3 |