Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #5822 | C2 | semidirect |
| 3. C2×#932 | C2 | semidirect |
| 4. #5745 | C2 | semidirect |
| 5. #5237 | C2 | semidirect |
| 6. C2×#833 | C2 | semidirect |
| 7. #5177 | C2 | semidirect |
| 8. #5160 | C2 | semidirect |
| 9. #5125 | C2 | semidirect |
| 16. C2×C3×SD16 | C22 | semidirect |
| 17. C2×C3×D8 | C22 | semidirect |
| 22. #942 | C22 | semidirect |
| 26. #932 | C22 | semidirect |
| 33. #901 | C22 | semidirect |
| 34. #836 | C22 | semidirect |
| 35. #833 | C22 | semidirect |
| 36. #833 | C22 | semidirect |
| 37. #819 | C22 | semidirect |
| 40. C2×AGL(1,ℤ/8) | D3 | semidirect |
| 106. C2×SD16 | C2×D3 | semidirect |
| 108. C2×D8 | C2×D3 | semidirect |
| 287. C3 | #3068 | 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 |
| #5822 | 2 |
| C2×#932 | 2 |
| #5745 | 2 |
| #5237 | 2 |
| C2×#833 | 2 |
| #5177 | 2 |
| #5160 | 2 |
| #5125 | 2 |
| #3068 | 3 |