Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #5197 | C2 | semidirect |
| 3. #4869 | C2 | semidirect |
| 4. C3×#360 | C2 | semidirect |
| 5. #4516 | C2 | semidirect |
| 6. #4512 | C2 | semidirect |
| 7. #4487 | C2 | semidirect |
| 16. #828 | C4 | semidirect |
| 17. #826 | C4 | semidirect |
| 27. #360 | D3 | semidirect |
| 32. C3×Q16 | C2×C4 | semidirect |
| 34. C3×D8 | C2×C4 | semidirect |
| 46. C3⋊C16 | C2×C4 | semidirect |
| 78. Q16 | C4×D3 | semidirect |
| 82. D8 | C4×D3 | semidirect |
| 132. C3 | AGL(1,ℤ/16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5197 | 2 |
| #5193 | 2 |
| #4869 | 2 |
| C3×#360 | 2 |
| #4516 | 2 |
| #4512 | 2 |
| #4487 | 2 |
| AGL(1,ℤ/16) | 3 |