Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. C3×#358 | C2 | semidirect |
| 5. #4564 | C2 | semidirect |
| 6. #4503 | C2 | semidirect |
| 7. #4492 | C2 | semidirect |
| 13. D3×Q16 | C4 | semidirect |
| 29. #358 | D3 | direct (N × H) |
| 39. C3×Q16 | C2×C4 | semidirect |
| 47. Dic12 | C2×C4 | semidirect |
| 97. Q16 | C4×D3 | semidirect |
| 140. D3 | #358 | direct (N × H) |
| 152. C3 | C2×#358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q16 | 2 |
| C2×D3×C16 | 2 |
| D3×#107 | 2 |
| C3×#358 | 2 |
| #4564 | 2 |
| #4503 | 2 |
| #4492 | 2 |
| C2×#358 | 3 |