Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
310 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 159 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×C3×C42 | C2 | semidirect |
| 3. C4×#67 | C2 | semidirect |
| 4. #926 | C2 | semidirect |
| 5. C4×D12 | C2 | semidirect |
| 6. #872 | C2 | semidirect |
| 7. C42×D3 | C2 | semidirect |
| 8. C4×Dic6 | C2 | semidirect |
| 13. #235 | C4 | direct (N × H) |
| 34. C2×C42 | D3 | semidirect |
| 38. C2×C3×C4 | C2×C4 | semidirect |
| 43. #67 | C2×C4 | semidirect |
| 46. D12 | C2×C4 | semidirect |
| 48. C4×D3 | C2×C4 | semidirect |
| 49. Dic6 | C2×C4 | semidirect |
| 75. C3×C4 | #41 | semidirect |
| 88. C2×C4 | C4×D3 | semidirect |
| 107. C4 | #235 | direct (N × H) |
| 108. C3 | C4×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#235 | 2 |
| C2×C3×C42 | 2 |
| C4×#67 | 2 |
| #926 | 2 |
| C4×D12 | 2 |
| #872 | 2 |
| C42×D3 | 2 |
| C4×Dic6 | 2 |
| C4×#41 | 3 |