Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 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. C22×C4×D3 | C2 | semidirect |
| 3. C3×C4×D4 | C2 | semidirect |
| 4. D4×Dic3 | C2 | semidirect |
| 5. C4×#67 | C2 | semidirect |
| 6. #893 | C2 | semidirect |
| 7. D3×C4⋊C4 | C2 | semidirect |
| 8. #67⋊C4 | C2 | semidirect |
| 9. D3×C22⋊C4 | C2 | semidirect |
| 10. C4×D12 | C2 | semidirect |
| 11. C42×D3 | C2 | semidirect |
| 15. C22×C3×C4 | C22 | semidirect |
| 17. C22×Dic3 | C22 | semidirect |
| 18. D3×D4 | C4 | direct (N × H) |
| 25. C2×C4×D3 | C22 | semidirect |
| 26. C2×C4×D3 | C22 | semidirect |
| 27. C3×C4⋊C4 | C22 | semidirect |
| 28. C3×C22⋊C4 | C22 | semidirect |
| 29. C3×C42 | C22 | semidirect |
| 30. #217 | C22 | semidirect |
| 31. (C2×D3)⋊C4 | C22 | semidirect |
| 32. (C2×D3)⋊C4 | C22 | semidirect |
| 33. C4⋊Dic3 | C22 | semidirect |
| 34. Dic3⋊C4 | C22 | semidirect |
| 35. C4×Dic3 | C22 | semidirect |
| 36. C4×Dic3 | C22 | semidirect |
| 37. C4×Dic3 | C22 | semidirect |
| 45. C4×D4 | D3 | direct (N × H) |
| 52. C22×D3 | C2×C4 | semidirect |
| 55. C3×D4 | C2×C4 | semidirect |
| 61. #67 | C2×C4 | semidirect |
| 67. D12 | C2×C4 | semidirect |
| 72. C4×D3 | C2×C4 | semidirect |
| 73. C4×D3 | D4 | direct (N × H) |
| 87. C22×C4 | C2×D3 | semidirect |
| 90. C4⋊C4 | C2×D3 | semidirect |
| 94. C22⋊C4 | C2×D3 | semidirect |
| 98. C42 | C2×D3 | semidirect |
| 101. C22×C3 | C22×C4 | semidirect |
| 107. C2×D3 | C22×C4 | semidirect |
| 112. C3×C4 | C22×C4 | semidirect |
| 113. C3×C4 | C2×D4 | semidirect |
| 116. Dic3 | C22×C4 | semidirect |
| 117. Dic3 | C2×D4 | semidirect |
| 126. D4 | C4×D3 | direct (N × H) |
| 148. D3 | C4×D4 | direct (N × H) |
| 158. C22 | C2×C4×D3 | semidirect |
| 166. C4 | C2×C4×D3 | semidirect |
| 167. C4 | D3×D4 | direct (N × H) |
| 168. C3 | C2×C4×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D4 | 2 |
| C22×C4×D3 | 2 |
| C3×C4×D4 | 2 |
| D4×Dic3 | 2 |
| C4×#67 | 2 |
| #893 | 2 |
| D3×C4⋊C4 | 2 |
| #67⋊C4 | 2 |
| D3×C22⋊C4 | 2 |
| C4×D12 | 2 |
| C42×D3 | 2 |
| C2×C4×D4 | 3 |