Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
426 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 215 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. C23×Dic3 | C2 | semidirect |
| 3. C2×#217 | C2 | semidirect |
| 4. D4×Dic3 | C2 | direct (N × H) |
| 5. C2×C4⋊Dic3 | C2 | semidirect |
| 6. C2×C4×Dic3 | C2 | semidirect |
| 9. C2×C3×D4 | C4 | semidirect |
| 16. C22×Dic3 | C22 | semidirect |
| 17. #217 | C22 | semidirect |
| 18. C4⋊Dic3 | C22 | semidirect |
| 19. C4×Dic3 | C22 | semidirect |
| 28. C23×C3 | C2×C4 | semidirect |
| 31. C3×D4 | C2×C4 | semidirect |
| 32. C2×C3×C4 | C2×C4 | semidirect |
| 37. C2×Dic3 | D4 | direct (N × H) |
| 42. C2×D4 | Dic3 | direct (N × H) |
| 57. C22×C3 | C22×C4 | semidirect |
| 61. C3×C4 | C22×C4 | semidirect |
| 64. Dic3 | C2×D4 | direct (N × H) |
| 67. C23 | C2×Dic3 | semidirect |
| 70. D4 | C2×Dic3 | direct (N × H) |
| 78. C2×C4 | C2×Dic3 | semidirect |
| 81. C2×C3 | C4×D4 | semidirect |
| 91. C22 | C22×Dic3 | semidirect |
| 96. C4 | C22×Dic3 | semidirect |
| 97. C3 | C2×C4×D4 | semidirect |
| 99. C2 | D4×Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D4 | 2 |
| C23×Dic3 | 2 |
| C2×#217 | 2 |
| D4×Dic3 | 2 |
| C2×C4⋊Dic3 | 2 |
| C2×C4×Dic3 | 2 |
| C2×C4×D4 | 3 |