Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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×#123 | C2 |
| hypercenter | #123 | D3 |
| hypocenter | C3 | #546 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D3×D4 | C2 | semidirect |
| 2. C2×#235 | C2 | semidirect |
| 3. C3×#123 | C2 | semidirect |
| 4. #939 | C2 | semidirect |
| 5. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 6. #896 | C2 | semidirect |
| 7. #895 | C2 | semidirect |
| 8. #894 | C2 | semidirect |
| 9. #893 | C2 | semidirect |
| 10. #885 | C2 | semidirect |
| 11. #884 | C2 | semidirect |
| 12. #882 | C2 | semidirect |
| 13. #882 | C2 | semidirect |
| 14. #67⋊C4 | C2 | semidirect |
| 15. D3×C22⋊C4 | C2 | semidirect |
| 20. C22×C3×C4 | C22 | semidirect |
| 23. C2×#67 | C22 | semidirect |
| 24. C2×#67 | C22 | semidirect |
| 25. C22×Dic3 | C22 | semidirect |
| 30. C2×D12 | C22 | semidirect |
| 31. C2×D12 | C22 | semidirect |
| 33. C2×C4×D3 | C22 | semidirect |
| 34. C2×C4×D3 | C22 | semidirect |
| 35. C2×C4×D3 | C22 | semidirect |
| 36. C2×Dic6 | C22 | semidirect |
| 37. C3×C4⋊C4 | C22 | semidirect |
| 38. C3×C4⋊C4 | C22 | semidirect |
| 39. C3×C22⋊C4 | C22 | semidirect |
| 40. C3×C22⋊C4 | C22 | semidirect |
| 41. C3×C22⋊C4 | C22 | semidirect |
| 42. #217 | C22 | semidirect |
| 46. (C2×D3)⋊C4 | C22 | semidirect |
| 47. (C2×D3)⋊C4 | C22 | semidirect |
| 48. (C2×D3)⋊C4 | C22 | semidirect |
| 49. (C2×D3)⋊C4 | C22 | semidirect |
| 50. (C2×D3)⋊C4 | C22 | semidirect |
| 51. Dic3⋊C4 | C22 | semidirect |
| 52. Dic3⋊C4 | C22 | semidirect |
| 53. C4×Dic3 | C22 | semidirect |
| 58. #123 | D3 | semidirect |
| 91. #67 | D4 | semidirect |
| 125. C22×C4 | C2×D3 | semidirect |
| 128. C4⋊C4 | C2×D3 | semidirect |
| 129. C4⋊C4 | C2×D3 | semidirect |
| 139. C22⋊C4 | C2×D3 | semidirect |
| 140. C22⋊C4 | C2×D3 | semidirect |
| 141. C22⋊C4 | C2×D3 | semidirect |
| 163. C2×D3 | #41 | semidirect |
| 249. C3 | #546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D4 | 2 |
| C2×#235 | 2 |
| C3×#123 | 2 |
| #939 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| #896 | 2 |
| #895 | 2 |
| #894 | 2 |
| #893 | 2 |
| #885 | 2 |
| #884 | 2 |
| #882 | 2 |
| #67⋊C4 | 2 |
| D3×C22⋊C4 | 2 |
| #546 | 3 |