Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×D3×Q8 | C2 | semidirect |
| 3. C2×C3×SD16 | C2 | semidirect |
| 4. C2×#215 | C2 | semidirect |
| 5. C2×#214 | C2 | semidirect |
| 6. D3×SD16 | C2 | direct (N × H) |
| 7. C2×#204 | C2 | semidirect |
| 8. C2×D3×C8 | C2 | semidirect |
| 11. C2×C3×Q8 | C22 | semidirect |
| 15. D3×Q8 | C22 | semidirect |
| 22. C2×Dic6 | C22 | semidirect |
| 23. C3×SD16 | C22 | semidirect |
| 24. C2×C3×C8 | C22 | semidirect |
| 25. #215 | C22 | semidirect |
| 26. #214 | C22 | semidirect |
| 27. C2×C3⋊C8 | C22 | semidirect |
| 28. #204 | C22 | semidirect |
| 29. D3×C8 | C22 | semidirect |
| 36. C2×SD16 | D3 | direct (N × H) |
| 44. C3×Q8 | C23 | semidirect |
| 59. Dic6 | C23 | semidirect |
| 60. C3×C8 | C23 | semidirect |
| 61. C3⋊C8 | C23 | semidirect |
| 67. C2×Q8 | C2×D3 | semidirect |
| 78. SD16 | C2×D3 | direct (N × H) |
| 81. C2×C8 | C2×D3 | semidirect |
| 88. C2×D3 | SD16 | direct (N × H) |
| 104. Q8 | C22×D3 | semidirect |
| 118. C8 | C22×D3 | semidirect |
| 120. C2×C3 | C2×SD16 | semidirect |
| 123. D3 | C2×SD16 | direct (N × H) |
| 137. C3 | C22×SD16 | semidirect |
| 141. C2 | D3×SD16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q8 | 2 |
| C2×D3×D4 | 2 |
| C2×C3×SD16 | 2 |
| C2×#215 | 2 |
| C2×#214 | 2 |
| D3×SD16 | 2 |
| C2×#204 | 2 |
| C2×D3×C8 | 2 |
| C22×SD16 | 3 |