Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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×C3×C4⋊Q8 | C2 | semidirect |
| 3. C2×Q8×Dic3 | C2 | semidirect |
| 4. #5731 | C2 | direct (N × H) |
| 6. C2×#889 | C2 | semidirect |
| 8. C2×#870 | C2 | semidirect |
| 12. C3×C4⋊Q8 | C22 | semidirect |
| 16. Q8×Dic3 | C22 | semidirect |
| 27. #889 | C22 | semidirect |
| 29. #870 | C22 | semidirect |
| 31. C2×C4⋊Q8 | D3 | semidirect |
| 62. C4⋊Q8 | C2×D3 | semidirect |
| 150. C2×C3 | #541 | semidirect |
| 166. C3 | C2×#541 | semidirect |
| 168. C2 | #5731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊Q8 | 2 |
| C2×#946 | 2 |
| C2×Q8×Dic3 | 2 |
| #5731 | 2 |
| C2×#898 | 2 |
| C2×#889 | 2 |
| C2×#872 | 2 |
| C2×#870 | 2 |
| C2×#541 | 3 |