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 |
| 4. #5228 | C2 | semidirect |
| 5. #5166 | C2 | semidirect |
| 6. Dic3×SD16 | C2 | semidirect |
| 8. #4799 | C2 | semidirect |
| 9. #4790 | C2 | semidirect |
| 10. #4721 | C2 | semidirect |
| 11. #4718 | C2 | 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 |
| #5600 | 2 |
| C3×#448 | 2 |
| #5228 | 2 |
| #5166 | 2 |
| Dic3×SD16 | 2 |
| #5033 | 2 |
| #4799 | 2 |
| #4790 | 2 |
| #4721 | 2 |
| #4718 | 2 |
| #3108 | 3 |