Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 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×Q16 | C2 | semidirect |
| 4. #5187 | C2 | semidirect |
| 5. #5027 | C2 | semidirect |
| 6. #5021 | C2 | semidirect |
| 7. #4882 | C2 | semidirect |
| 8. #4812 | C2 | semidirect |
| 9. #4803 | C2 | semidirect |
| 10. #4694 | C2 | semidirect |
| 11. #4688 | C2 | semidirect |
| 50. C4×Q16 | D3 | semidirect |
| 251. C3 | #3333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5579 | 2 |
| #5577 | 2 |
| C3×C4×Q16 | 2 |
| #5187 | 2 |
| #5027 | 2 |
| #5021 | 2 |
| #4882 | 2 |
| #4812 | 2 |
| #4803 | 2 |
| #4694 | 2 |
| #4688 | 2 |
| #3333 | 3 |