Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5570 | C2 | semidirect |
| 5. #5021 | C2 | semidirect |
| 7. #4858 | C2 | semidirect |
| 8. #4799 | C2 | semidirect |
| 10. #4680 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 60. C3×SD16 | Q8 | semidirect |
| 143. SD16 | Dic6 | semidirect |
| 224. C3 | #3381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5570 | 2 |
| #5543 | 2 |
| C3×C4×SD16 | 2 |
| Dic3×SD16 | 2 |
| #5021 | 2 |
| #5007 | 2 |
| #4858 | 2 |
| #4799 | 2 |
| #4763 | 2 |
| #4680 | 2 |
| C8×Dic6 | 2 |
| #3381 | 3 |