Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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 |
|---|---|---|
| 2. #5819 | C2 | semidirect |
| 3. C2×#837 | C2 | semidirect |
| 4. #5197 | C2 | semidirect |
| 5. #5196 | C2 | semidirect |
| 6. #5125 | C2 | semidirect |
| 7. Dic3×M16 | C2 | semidirect |
| 10. C3×#137 | C4 | semidirect |
| 11. C3×AGL(1,ℤ/8) | C4 | semidirect |
| 15. #948 | C22 | semidirect |
| 20. #837 | C22 | semidirect |
| 21. #837 | C22 | semidirect |
| 22. #819 | C22 | semidirect |
| 23. #815 | C22 | semidirect |
| 24. C8×Dic3 | C22 | semidirect |
| 42. C3×Q16 | C2×C4 | semidirect |
| 43. C3×SD16 | C2×C4 | semidirect |
| 44. C3×D8 | C2×C4 | semidirect |
| 58. #137 | Dic3 | semidirect |
| 59. AGL(1,ℤ/8) | Dic3 | semidirect |
| 104. Q16 | C2×Dic3 | semidirect |
| 105. SD16 | C2×Dic3 | semidirect |
| 106. D8 | C2×Dic3 | semidirect |
| 166. C3 | #2956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#575 | 2 |
| #5819 | 2 |
| C2×#837 | 2 |
| #5197 | 2 |
| #5196 | 2 |
| #5125 | 2 |
| Dic3×M16 | 2 |
| #2956 | 3 |