Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×Q8×Dic3 | C2 | semidirect |
| 3. C3×#451 | C2 | semidirect |
| 5. #5185 | C2 | semidirect |
| 6. Dic3×Q16 | C2 | semidirect |
| 7. #5043 | C2 | semidirect |
| 8. #4796 | C2 | semidirect |
| 9. #4788 | C2 | semidirect |
| 11. #4718 | C2 | semidirect |
| 50. #451 | D3 | semidirect |
| 257. C3 | #3108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic3 | 2 |
| #5624 | 2 |
| C3×#451 | 2 |
| #5227 | 2 |
| #5185 | 2 |
| Dic3×Q16 | 2 |
| #5043 | 2 |
| #4796 | 2 |
| #4788 | 2 |
| #4736 | 2 |
| #4718 | 2 |
| #3108 | 3 |