Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×D3×Q8 | C2 | semidirect |
| 3. C3×#137 | C2 | semidirect |
| 4. #951 | C2 | semidirect |
| 5. #942 | C2 | semidirect |
| 6. #918 | C2 | semidirect |
| 7. D3×Q16 | C2 | semidirect |
| 8. #915 | C2 | semidirect |
| 9. D3×SD16 | C2 | semidirect |
| 10. #909 | C2 | semidirect |
| 11. D3×M16 | C2 | semidirect |
| 14. C2×C3×Q8 | C22 | semidirect |
| 20. D3×Q8 | C22 | semidirect |
| 31. C2×Dic6 | C22 | semidirect |
| 32. C3×Q16 | C22 | semidirect |
| 33. C3×SD16 | C22 | semidirect |
| 34. C3×M16 | C22 | semidirect |
| 35. #216 | C22 | semidirect |
| 36. #216 | C22 | semidirect |
| 37. #215 | C22 | semidirect |
| 38. #214 | C22 | semidirect |
| 39. #208 | C22 | semidirect |
| 40. Dic12 | C22 | semidirect |
| 41. #204 | C22 | semidirect |
| 42. ΓL(1,𝔽25) | C22 | semidirect |
| 51. #137 | D3 | direct (N × H) |
| 103. C2×Q8 | C2×D3 | semidirect |
| 112. Q16 | C2×D3 | semidirect |
| 116. SD16 | C2×D3 | semidirect |
| 119. M16 | C2×D3 | semidirect |
| 176. D3 | #137 | direct (N × H) |
| 192. C3 | C2×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#41 | 2 |
| C2×D3×Q8 | 2 |
| C3×#137 | 2 |
| #951 | 2 |
| #942 | 2 |
| #918 | 2 |
| D3×Q16 | 2 |
| #915 | 2 |
| D3×SD16 | 2 |
| #909 | 2 |
| D3×M16 | 2 |
| C2×#137 | 3 |