Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #5833 | C2 | semidirect |
| 3. C2×#932 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. #5221 | C2 | semidirect |
| 6. C2×#825 | C2 | semidirect |
| 7. #4554 | C2 | semidirect |
| 33. C2×AGL(1,ℤ/8) | D3 | semidirect |
| 52. C2×C3×D4 | D4 | semidirect |
| 69. C3×M16 | D4 | semidirect |
| 82. #208 | D4 | semidirect |
| 172. C2×D4 | #67 | semidirect |
| 185. M16 | #67 | semidirect |
| 296. C3 | #2006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×AGL(1,ℤ/8) | 2 |
| #5833 | 2 |
| C2×#932 | 2 |
| C2×#837 | 2 |
| #5221 | 2 |
| C2×#825 | 2 |
| #4554 | 2 |
| #2006 | 3 |