Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
426 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4 | C22 |
| commutator | C2 | C23×C3×C4 |
| Frattini, cosocle | C22 | C24×C3 |
| socle | C23×C3 | C23 |
| prime radical | C22×C3×D4 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C3×C4 | C2 | semidirect |
| 3. C3×C4×D4 | C2 | direct (N × H) |
| 4. C2×C3×C4⋊C4 | C2 | semidirect |
| 5. C2×C3×C22⋊C4 | C2 | semidirect |
| 6. C2×C3×C42 | C2 | semidirect |
| 7. C2×C4×D4 | C3 | direct (N × H) |
| 9. C2×C3×D4 | C4 | direct (N × H) |
| 16. C22×C3×C4 | C22 | semidirect |
| 17. C3×C4⋊C4 | C22 | semidirect |
| 18. C3×C22⋊C4 | C22 | semidirect |
| 19. C3×C42 | C22 | semidirect |
| 21. C23×C4 | C2×C3 | semidirect |
| 22. C4×D4 | C2×C3 | direct (N × H) |
| 23. C2×C4⋊C4 | C2×C3 | semidirect |
| 24. C2×C22⋊C4 | C2×C3 | semidirect |
| 25. C2×C42 | C2×C3 | semidirect |
| 28. C23×C3 | C2×C4 | semidirect |
| 31. C3×D4 | C2×C4 | direct (N × H) |
| 35. C2×C3×C4 | C2×C4 | semidirect |
| 36. C2×C3×C4 | D4 | direct (N × H) |
| 42. C2×D4 | C3×C4 | direct (N × H) |
| 49. C22×C4 | C22×C3 | semidirect |
| 50. C4⋊C4 | C22×C3 | semidirect |
| 51. C22⋊C4 | C22×C3 | semidirect |
| 52. C42 | C22×C3 | semidirect |
| 57. C22×C3 | C22×C4 | semidirect |
| 63. C3×C4 | C22×C4 | semidirect |
| 64. C3×C4 | C2×D4 | direct (N × H) |
| 67. C23 | C2×C3×C4 | semidirect |
| 70. D4 | C2×C3×C4 | direct (N × H) |
| 74. C2×C4 | C2×C3×C4 | semidirect |
| 75. C2×C4 | C3×D4 | direct (N × H) |
| 81. C2×C3 | C4×D4 | direct (N × H) |
| 89. C22 | C22×C3×C4 | semidirect |
| 95. C4 | C22×C3×C4 | semidirect |
| 96. C4 | C2×C3×D4 | direct (N × H) |
| 97. C3 | C2×C4×D4 | direct (N × H) |
| 99. C2 | C3×C4×D4 | 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×C3×C4 | 2 |
| C3×C4×D4 | 2 |
| C2×C3×C4⋊C4 | 2 |
| C2×C3×C22⋊C4 | 2 |
| C2×C3×C42 | 2 |
| C2×C4×D4 | 3 |