Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
170 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4×Dic3 | C2 | semidirect |
| 3. C2×#208 | C2 | semidirect |
| 4. #837 | C2 | direct (N × H) |
| 8. C3×#41 | C4 | semidirect |
| 10. C2×C3×Q8 | C4 | semidirect |
| 12. C2×C3×D4 | C4 | semidirect |
| 17. C4×Dic3 | C22 | semidirect |
| 19. #208 | C22 | semidirect |
| 28. C3×Q8 | C2×C4 | semidirect |
| 32. C3×D4 | C2×C4 | semidirect |
| 47. #41 | Dic3 | semidirect |
| 49. C2×Q8 | Dic3 | semidirect |
| 51. C2×D4 | Dic3 | semidirect |
| 75. Q8 | C2×Dic3 | semidirect |
| 79. D4 | C2×Dic3 | semidirect |
| 95. C2×C3 | #104 | semidirect |
| 109. C3 | C2×#104 | semidirect |
| 113. C2 | #837 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41 | 2 |
| C2×C4×Dic3 | 2 |
| C2×#208 | 2 |
| #837 | 2 |
| C2×#104 | 3 |