Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. C3×#532 | C2 | semidirect |
| 2. #5479 | C2 | semidirect |
| 3. #5089 | C2 | semidirect |
| 4. #5081 | C2 | semidirect |
| 5. #5074 | C2 | semidirect |
| 6. #5071 | C2 | semidirect |
| 7. #5042 | C2 | semidirect |
| 8. #5039 | C2 | semidirect |
| 9. C4×#214 | C2 | semidirect |
| 10. C4×#213 | C2 | semidirect |
| 11. C4×#208 | C2 | semidirect |
| 44. #532 | D3 | semidirect |
| 153. C3⋊C8 | #41 | semidirect |
| 268. C3 | #3171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| #5479 | 2 |
| #5089 | 2 |
| #5081 | 2 |
| #5074 | 2 |
| #5071 | 2 |
| #5042 | 2 |
| #5039 | 2 |
| C4×#214 | 2 |
| C4×#213 | 2 |
| C4×#208 | 2 |
| #3171 | 3 |