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×#235 | C2 | semidirect |
| 2. C22×D12 | C2 | semidirect |
| 3. C2×C3×M16 | C2 | semidirect |
| 4. #908 | C2 | direct (N × H) |
| 5. C2×D24 | C2 | semidirect |
| 6. C2×#204 | C2 | semidirect |
| 12. #235 | C22 | semidirect |
| 16. C2×D12 | C22 | semidirect |
| 17. C2×D12 | C22 | semidirect |
| 19. C2×Dic6 | C22 | semidirect |
| 20. C3×M16 | C22 | semidirect |
| 21. C2×C3×C8 | C22 | semidirect |
| 22. D24 | C22 | semidirect |
| 23. #204 | C22 | semidirect |
| 29. C2×M16 | D3 | semidirect |
| 45. D12 | C23 | semidirect |
| 48. Dic6 | C23 | semidirect |
| 49. C3×C8 | C23 | semidirect |
| 64. M16 | C2×D3 | semidirect |
| 65. C2×C8 | C2×D3 | semidirect |
| 97. C8 | C22×D3 | semidirect |
| 99. C2×C3 | AGL(1,ℤ/8) | semidirect |
| 115. C3 | C2×AGL(1,ℤ/8) | semidirect |
| 119. C2 | #908 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#235 | 2 |
| C22×D12 | 2 |
| C2×C3×M16 | 2 |
| #908 | 2 |
| C2×D24 | 2 |
| C2×#204 | 2 |
| C2×AGL(1,ℤ/8) | 3 |