Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×C3×#41 | C2 | semidirect |
| 2. C22×D12 | C2 | semidirect |
| 3. #949 | C2 | direct (N × H) |
| 4. C2×#215 | C2 | semidirect |
| 5. C2×#213 | C2 | semidirect |
| 6. C2×#208 | C2 | semidirect |
| 10. C3×#41 | C22 | semidirect |
| 11. C2×C3×Q8 | C22 | semidirect |
| 13. C2×C3×D4 | C22 | semidirect |
| 19. C2×D12 | C22 | semidirect |
| 20. #215 | C22 | semidirect |
| 21. #213 | C22 | semidirect |
| 22. #208 | C22 | semidirect |
| 23. C2×C3⋊C8 | C22 | semidirect |
| 24. C2×#41 | D3 | semidirect |
| 36. C3×Q8 | C23 | semidirect |
| 39. C3×D4 | C23 | semidirect |
| 49. C3⋊C8 | C23 | semidirect |
| 52. #41 | C2×D3 | semidirect |
| 53. C2×Q8 | C2×D3 | semidirect |
| 59. C2×D4 | C2×D3 | semidirect |
| 84. Q8 | C22×D3 | semidirect |
| 90. D4 | C22×D3 | semidirect |
| 100. C2×C3 | AGL(1,ℤ/8) | semidirect |
| 115. C3 | C2×AGL(1,ℤ/8) | semidirect |
| 119. C2 | #949 | 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 |
| C22×D12 | 2 |
| #949 | 2 |
| C2×#215 | 2 |
| C2×#213 | 2 |
| C2×#208 | 2 |
| C2×AGL(1,ℤ/8) | 3 |