Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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. D3×M16 | C2 | semidirect |
| 3. C42×D3 | C2 | semidirect |
| 4. C3×#104 | C2 | semidirect |
| 5. #837 | C2 | semidirect |
| 6. #825 | C2 | semidirect |
| 7. #805 | C2 | semidirect |
| 10. #239 | C4 | semidirect |
| 11. D3×Q8 | C4 | semidirect |
| 13. #237 | C4 | semidirect |
| 15. D3×D4 | C4 | semidirect |
| 21. C3×M16 | C22 | semidirect |
| 22. C3×C42 | C22 | semidirect |
| 24. C4×Dic3 | C22 | semidirect |
| 25. #208 | C22 | semidirect |
| 34. #104 | D3 | direct (N × H) |
| 37. C3×Q8 | C2×C4 | semidirect |
| 39. C3×D4 | C2×C4 | semidirect |
| 50. D12 | C2×C4 | semidirect |
| 60. Dic6 | C2×C4 | semidirect |
| 77. M16 | C2×D3 | semidirect |
| 81. C42 | C2×D3 | semidirect |
| 101. Q8 | C4×D3 | semidirect |
| 108. D4 | C4×D3 | semidirect |
| 130. D3 | #104 | direct (N × H) |
| 146. C3 | C2×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#41 | 2 |
| D3×M16 | 2 |
| C42×D3 | 2 |
| C3×#104 | 2 |
| #837 | 2 |
| #825 | 2 |
| #805 | 2 |
| C2×#104 | 3 |