Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 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×#126 | C2 |
| prime radical | #882 | C2 |
| hypercenter | #126 | D3 |
| hypocenter | C3 | #551 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#126 | C2 | semidirect |
| 2. #897 | C2 | semidirect |
| 3. #896 | C2 | semidirect |
| 4. #894 | C2 | semidirect |
| 5. #894 | C2 | semidirect |
| 6. #893 | C2 | semidirect |
| 7. #892 | C2 | semidirect |
| 8. #885 | C2 | semidirect |
| 9. #883 | C2 | semidirect |
| 11. D3×C22⋊C4 | C2 | semidirect |
| 12. D3×C22⋊C4 | C2 | semidirect |
| 13. #879 | C2 | semidirect |
| 14. C4×D12 | C2 | semidirect |
| 15. #872 | C2 | semidirect |
| 25. C2×C4×D3 | C22 | semidirect |
| 26. C2×Dic6 | C22 | semidirect |
| 27. C3×C4⋊C4 | C22 | semidirect |
| 28. C3×C4⋊C4 | C22 | semidirect |
| 29. C3×C4⋊C4 | C22 | semidirect |
| 33. C3×C42 | C22 | semidirect |
| 42. (C2×D3)⋊C4 | C22 | semidirect |
| 43. (C2×D3)⋊C4 | C22 | semidirect |
| 44. (C2×D3)⋊C4 | C22 | semidirect |
| 45. C4⋊Dic3 | C22 | semidirect |
| 46. C4⋊Dic3 | C22 | semidirect |
| 47. Dic3⋊C4 | C22 | semidirect |
| 48. Dic3⋊C4 | C22 | semidirect |
| 49. Dic3⋊C4 | C22 | semidirect |
| 50. C4×Dic3 | C22 | semidirect |
| 51. C4×Dic3 | C22 | semidirect |
| 53. #126 | D3 | semidirect |
| 109. C4⋊C4 | C2×D3 | semidirect |
| 110. C4⋊C4 | C2×D3 | semidirect |
| 111. C4⋊C4 | C2×D3 | semidirect |
| 128. C42 | C2×D3 | semidirect |
| 213. C3 | #551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#126 | 2 |
| #897 | 2 |
| #896 | 2 |
| #894 | 2 |
| #893 | 2 |
| #892 | 2 |
| #885 | 2 |
| #883 | 2 |
| #882 | 2 |
| D3×C22⋊C4 | 2 |
| #879 | 2 |
| C4×D12 | 2 |
| #872 | 2 |
| #551 | 3 |