Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5567 | C2 | semidirect |
| 3. C3×C4×SD16 | C2 | semidirect |
| 4. #5175 | C2 | semidirect |
| 5. #5027 | C2 | semidirect |
| 6. #5019 | C2 | semidirect |
| 7. #4852 | C2 | semidirect |
| 8. #4818 | C2 | semidirect |
| 9. #4762 | C2 | semidirect |
| 10. #4693 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 52. C4×SD16 | D3 | semidirect |
| 143. Dic6 | SD16 | semidirect |
| 145. C3×C8 | #41 | semidirect |
| 228. C8 | #235 | semidirect |
| 251. C3 | #3392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5567 | 2 |
| #5553 | 2 |
| C3×C4×SD16 | 2 |
| #5175 | 2 |
| #5027 | 2 |
| #5019 | 2 |
| #4852 | 2 |
| #4818 | 2 |
| #4762 | 2 |
| #4693 | 2 |
| C8×Dic6 | 2 |
| #3392 | 3 |