Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5579 | C2 | semidirect |
| 3. C3×C4×SD16 | C2 | semidirect |
| 4. #5174 | C2 | semidirect |
| 5. #5021 | C2 | semidirect |
| 6. #5008 | C2 | semidirect |
| 7. #4861 | C2 | semidirect |
| 8. #4814 | C2 | semidirect |
| 9. #4774 | C2 | semidirect |
| 10. #4688 | C2 | semidirect |
| 11. #4682 | C2 | semidirect |
| 50. C4×SD16 | D3 | semidirect |
| 237. C3 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5579 | 2 |
| #5563 | 2 |
| C3×C4×SD16 | 2 |
| #5174 | 2 |
| #5021 | 2 |
| #5008 | 2 |
| #4861 | 2 |
| #4814 | 2 |
| #4774 | 2 |
| #4688 | 2 |
| #4682 | 2 |
| #3357 | 3 |