Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 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. Dic3×Q16 | C2 | semidirect |
| 4. C3×#358 | C2 | semidirect |
| 6. #4502 | C2 | semidirect |
| 7. #4489 | C2 | semidirect |
| 16. #828 | C4 | semidirect |
| 25. #358 | D3 | semidirect |
| 32. C3×Q16 | C2×C4 | semidirect |
| 44. C3⋊C16 | C2×C4 | semidirect |
| 76. Q16 | C4×D3 | semidirect |
| 130. C3 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×Q16 | 2 |
| C2×#828 | 2 |
| #4872 | 2 |
| C3×#358 | 2 |
| #4509 | 2 |
| #4502 | 2 |
| #4489 | 2 |
| #2175 | 3 |