Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
1362 conjugacy classes of subgroups; only the 503 normal subgroups are shown.
This group has 1362 conjugacy classes of subgroups — too many to draw. Only its 503 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D3 |
| commutator, cosocle | C2×C3 | C25 |
| Frattini | C2 | C24×D3 |
| Fitting | C22×C3×D4 | C2 |
| socle | C23×C3 | C23 |
| hypercenter | C22×D4 | D3 |
| hypocenter | C3 | C23×D4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D3 | C2 | semidirect |
| 2. C22×C3×D4 | C2 | semidirect |
| 3. C22×#67 | C2 | semidirect |
| 4. C2×D3×D4 | C2 | direct (N × H) |
| 5. C22×D12 | C2 | semidirect |
| 6. C22×C4×D3 | C2 | semidirect |
| 8. C24×C3 | C22 | semidirect |
| 11. C23×D3 | C22 | semidirect |
| 12. C23×D3 | C22 | semidirect |
| 13. C2×C3×D4 | C22 | semidirect |
| 14. C22×C3×C4 | C22 | semidirect |
| 15. C2×#67 | C22 | semidirect |
| 16. C22×Dic3 | C22 | semidirect |
| 17. D3×D4 | C22 | direct (N × H) |
| 18. C2×D12 | C22 | semidirect |
| 19. C2×C4×D3 | C22 | semidirect |
| 24. C22×D4 | D3 | direct (N × H) |
| 28. C23×C3 | C23 | semidirect |
| 31. C22×D3 | D4 | direct (N × H) |
| 33. C22×D3 | C23 | semidirect |
| 34. C22×D3 | C23 | semidirect |
| 35. C3×D4 | C23 | semidirect |
| 36. C2×C3×C4 | C23 | semidirect |
| 37. #67 | C23 | semidirect |
| 38. C2×Dic3 | C23 | semidirect |
| 39. D12 | C23 | semidirect |
| 40. C4×D3 | C23 | semidirect |
| 45. C24 | C2×D3 | semidirect |
| 49. C2×D4 | C2×D3 | direct (N × H) |
| 52. C22×C4 | C2×D3 | semidirect |
| 54. C22×C3 | C2×D4 | semidirect |
| 56. C22×C3 | C24 | semidirect |
| 59. C2×D3 | C2×D4 | direct (N × H) |
| 61. C2×D3 | C24 | semidirect |
| 62. C3×C4 | C24 | semidirect |
| 63. Dic3 | C24 | semidirect |
| 72. C23 | C22×D3 | semidirect |
| 75. D4 | C22×D3 | direct (N × H) |
| 78. C2×C4 | C22×D3 | semidirect |
| 80. C2×C3 | C22×D4 | semidirect |
| 83. D3 | C22×D4 | direct (N × H) |
| 90. C22 | D3×D4 | direct (N × H) |
| 92. C22 | C23×D3 | semidirect |
| 94. C4 | C23×D3 | semidirect |
| 95. C3 | C23×D4 | semidirect |
| 99. C2 | C2×D3×D4 | 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×C3×D4 | 2 |
| C22×#67 | 2 |
| C2×D3×D4 | 2 |
| C22×D12 | 2 |
| C22×C4×D3 | 2 |
| C23×D4 | 3 |