Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Fitting | C3×#121 | C2 |
| hypercenter | #121 | D3 |
| hypocenter | C3 | C2×#121 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D3×D4 | C2 | semidirect |
| 2. C2×D3×D4 | C2 | semidirect |
| 3. C22×C4×D3 | C2 | semidirect |
| 4. C3×#121 | C2 | semidirect |
| 5. #939 | C2 | semidirect |
| 6. #938 | C2 | semidirect |
| 7. #930 | C2 | semidirect |
| 8. #895 | C2 | semidirect |
| 9. D3×C4⋊C4 | C2 | semidirect |
| 10. #884 | C2 | semidirect |
| 11. D3×C22⋊C4 | C2 | semidirect |
| 15. C2×C3×D4 | C22 | semidirect |
| 16. C2×C3×D4 | C22 | semidirect |
| 17. C22×C3×C4 | C22 | semidirect |
| 18. C2×#67 | C22 | semidirect |
| 19. C2×#67 | C22 | semidirect |
| 20. C2×#67 | C22 | semidirect |
| 21. C22×Dic3 | C22 | semidirect |
| 24. C2×D12 | C22 | semidirect |
| 25. C2×D12 | C22 | semidirect |
| 30. C2×C4×D3 | C22 | semidirect |
| 31. C2×C4×D3 | C22 | semidirect |
| 32. C3×C4⋊C4 | C22 | semidirect |
| 33. C3×C22⋊C4 | C22 | semidirect |
| 34. #217 | C22 | semidirect |
| 35. (C2×D3)⋊C4 | C22 | semidirect |
| 36. (C2×D3)⋊C4 | C22 | semidirect |
| 37. C4⋊Dic3 | C22 | semidirect |
| 38. Dic3⋊C4 | C22 | semidirect |
| 47. #121 | D3 | direct (N × H) |
| 57. C22×D3 | D4 | semidirect |
| 80. C4×D3 | D4 | semidirect |
| 90. C2×D4 | C2×D3 | semidirect |
| 91. C2×D4 | C2×D3 | semidirect |
| 99. C22×C4 | C2×D3 | semidirect |
| 102. C4⋊C4 | C2×D3 | semidirect |
| 106. C22⋊C4 | C2×D3 | semidirect |
| 112. C22×C3 | C2×D4 | semidirect |
| 123. C2×D3 | C2×D4 | semidirect |
| 127. C3×C4 | C2×D4 | semidirect |
| 130. Dic3 | C2×D4 | semidirect |
| 169. D3 | #121 | direct (N × H) |
| 186. C22 | D3×D4 | semidirect |
| 193. C4 | D3×D4 | semidirect |
| 194. C3 | C2×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D4 | 2 |
| C22×C4×D3 | 2 |
| C3×#121 | 2 |
| #939 | 2 |
| #938 | 2 |
| #930 | 2 |
| #895 | 2 |
| D3×C4⋊C4 | 2 |
| #884 | 2 |
| D3×C22⋊C4 | 2 |
| C2×#121 | 3 |