Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
674 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 207 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. C22×C4×D3 | C2 | semidirect |
| 3. C2×C3×C22⋊C4 | C2 | semidirect |
| 4. C2×#217 | C2 | semidirect |
| 5. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 6. D3×C22⋊C4 | C2 | direct (N × H) |
| 10. C23×D3 | C4 | semidirect |
| 14. C22×C3×C4 | C22 | semidirect |
| 15. C22×Dic3 | C22 | semidirect |
| 17. C2×C4×D3 | C22 | semidirect |
| 18. C3×C22⋊C4 | C22 | semidirect |
| 19. #217 | C22 | semidirect |
| 20. (C2×D3)⋊C4 | C22 | semidirect |
| 26. C2×C22⋊C4 | D3 | direct (N × H) |
| 28. C23×C3 | C2×C4 | semidirect |
| 35. C22×D3 | C2×C4 | semidirect |
| 36. C22×D3 | C2×C4 | semidirect |
| 41. C2×C3×C4 | C23 | semidirect |
| 43. C2×Dic3 | C23 | semidirect |
| 54. C22×C4 | C2×D3 | semidirect |
| 57. C22⋊C4 | C2×D3 | direct (N × H) |
| 61. C22×C3 | C22×C4 | semidirect |
| 67. C2×D3 | C22⋊C4 | direct (N × H) |
| 69. C2×D3 | C22×C4 | semidirect |
| 83. C23 | C4×D3 | semidirect |
| 90. C2×C4 | C22×D3 | semidirect |
| 92. C2×C3 | C2×C22⋊C4 | semidirect |
| 96. D3 | C2×C22⋊C4 | direct (N × H) |
| 107. C22 | C2×C4×D3 | semidirect |
| 112. C3 | C22×C22⋊C4 | semidirect |
| 116. C2 | D3×C22⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D3 | 2 |
| C22×C4×D3 | 2 |
| C2×C3×C22⋊C4 | 2 |
| C2×#217 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| D3×C22⋊C4 | 2 |
| C22×C22⋊C4 | 3 |