Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D3 |
| commutator, cosocle | C2×C3 | C25 |
| Frattini | C2 | C24×D3 |
| Fitting | C2×C3×#41 | C2 |
| socle | C22×C3 | C24 |
| hypercenter | C2×#41 | D3 |
| hypocenter | C3 | C22×#41 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#41 | C2 | semidirect |
| 2. D3×#41 | C2 | direct (N × H) |
| 3. C2×#239 | C2 | semidirect |
| 4. C2×D3×Q8 | C2 | semidirect |
| 5. C2×#237 | C2 | semidirect |
| 6. C2×D3×D4 | C2 | semidirect |
| 7. C2×#235 | C2 | semidirect |
| 8. C22×C4×D3 | C2 | semidirect |
| 11. C3×#41 | C22 | semidirect |
| 12. C2×C3×Q8 | 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. #239 | C22 | semidirect |
| 18. D3×Q8 | C22 | semidirect |
| 19. #237 | C22 | semidirect |
| 20. D3×D4 | C22 | semidirect |
| 21. #235 | C22 | semidirect |
| 22. C2×D12 | C22 | semidirect |
| 25. C2×C4×D3 | C22 | semidirect |
| 26. C2×C4×D3 | C22 | semidirect |
| 27. C2×C4×D3 | C22 | semidirect |
| 28. C2×Dic6 | C22 | semidirect |
| 33. C2×#41 | D3 | direct (N × H) |
| 42. C3×Q8 | C23 | semidirect |
| 43. C3×D4 | C23 | semidirect |
| 46. C2×C3×C4 | C23 | semidirect |
| 47. #67 | C23 | semidirect |
| 50. C2×Dic3 | C23 | semidirect |
| 51. D12 | C23 | semidirect |
| 54. C4×D3 | C23 | semidirect |
| 55. C4×D3 | C23 | semidirect |
| 56. Dic6 | C23 | semidirect |
| 61. #41 | C2×D3 | direct (N × H) |
| 64. C2×Q8 | C2×D3 | semidirect |
| 68. C2×D4 | C2×D3 | semidirect |
| 75. C22×C4 | C2×D3 | semidirect |
| 81. C2×D3 | #41 | direct (N × H) |
| 94. Q8 | C22×D3 | semidirect |
| 97. D4 | C22×D3 | semidirect |
| 107. C2×C4 | C22×D3 | semidirect |
| 109. C2×C3 | C2×#41 | semidirect |
| 112. D3 | C2×#41 | direct (N × H) |
| 125. C3 | C22×#41 | semidirect |
| 129. C2 | D3×#41 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41 | 2 |
| D3×#41 | 2 |
| C2×#239 | 2 |
| C2×D3×Q8 | 2 |
| C2×#237 | 2 |
| C2×D3×D4 | 2 |
| C2×#235 | 2 |
| C22×C4×D3 | 2 |
| C22×#41 | 3 |