Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
426 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 183 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. C23×C3×C4 | C2 | semidirect |
| 3. C22×C4×D3 | C2 | semidirect |
| 4. C2×#217 | C2 | semidirect |
| 5. C4×#67 | C2 | direct (N × H) |
| 6. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C2×Dic3⋊C4 | C2 | semidirect |
| 8. C2×C4×Dic3 | C2 | semidirect |
| 15. C22×C3×C4 | C22 | semidirect |
| 16. C2×#67 | C4 | direct (N × H) |
| 22. C2×C4×D3 | C22 | semidirect |
| 23. #217 | C22 | semidirect |
| 24. (C2×D3)⋊C4 | C22 | semidirect |
| 25. Dic3⋊C4 | C22 | semidirect |
| 26. C4×Dic3 | C22 | semidirect |
| 29. C23×C4 | D3 | semidirect |
| 37. C23×C3 | C2×C4 | semidirect |
| 42. C22×D3 | C2×C4 | semidirect |
| 46. C2×C3×C4 | D4 | semidirect |
| 49. #67 | C2×C4 | direct (N × H) |
| 52. C2×Dic3 | C2×C4 | semidirect |
| 69. C22×C4 | C2×D3 | semidirect |
| 78. C22×C3 | C22×C4 | semidirect |
| 85. C2×D3 | C22×C4 | semidirect |
| 87. C3×C4 | C2×D4 | semidirect |
| 90. Dic3 | C22×C4 | semidirect |
| 97. C23 | C4×D3 | semidirect |
| 110. C2×C4 | #67 | direct (N × H) |
| 114. C2×C3 | C4×D4 | semidirect |
| 127. C22 | C2×C4×D3 | semidirect |
| 135. C4 | C2×#67 | direct (N × H) |
| 136. C3 | C2×C4×D4 | semidirect |
| 139. C2 | C4×#67 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4 | 2 |
| C22×#67 | 2 |
| C22×C4×D3 | 2 |
| C2×#217 | 2 |
| C4×#67 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| C2×Dic3⋊C4 | 2 |
| C2×C4×Dic3 | 2 |
| C2×C4×D4 | 3 |