Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#239 | C2 | semidirect |
| 2. C2×D3×D4 | C2 | semidirect |
| 3. C2×C3×SD16 | C2 | semidirect |
| 4. C2×#215 | C2 | semidirect |
| 5. C2×#213 | C2 | semidirect |
| 6. #914 | C2 | direct (N × H) |
| 7. C2×D24 | C2 | semidirect |
| 8. C2×ΓL(1,𝔽25) | C2 | semidirect |
| 11. C2×C3×Q8 | C22 | semidirect |
| 15. #239 | C22 | semidirect |
| 17. D3×D4 | C22 | semidirect |
| 20. C2×D12 | C22 | semidirect |
| 23. C3×SD16 | C22 | semidirect |
| 24. C2×C3×C8 | C22 | semidirect |
| 25. #215 | C22 | semidirect |
| 26. #213 | C22 | semidirect |
| 27. C2×C3⋊C8 | C22 | semidirect |
| 28. D24 | C22 | semidirect |
| 29. ΓL(1,𝔽25) | C22 | semidirect |
| 34. C2×SD16 | D3 | semidirect |
| 45. C3×Q8 | C23 | semidirect |
| 56. D12 | C23 | semidirect |
| 60. C3×C8 | C23 | semidirect |
| 61. C3⋊C8 | C23 | semidirect |
| 65. C2×Q8 | C2×D3 | semidirect |
| 76. SD16 | C2×D3 | semidirect |
| 81. C2×C8 | C2×D3 | semidirect |
| 103. Q8 | C22×D3 | semidirect |
| 119. C8 | C22×D3 | semidirect |
| 121. C2×C3 | AGL(1,ℤ/8) | semidirect |
| 140. C3 | C2×AGL(1,ℤ/8) | semidirect |
| 145. C2 | #914 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#239 | 2 |
| C2×D3×D4 | 2 |
| C2×C3×SD16 | 2 |
| C2×#215 | 2 |
| C2×#213 | 2 |
| #914 | 2 |
| C2×D24 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| C2×AGL(1,ℤ/8) | 3 |