Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
| hypercenter | #126 | D3 |
| hypocenter | C3 | #538 |
| 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. #898 | C2 | semidirect |
| 3. #896 | C2 | semidirect |
| 4. #895 | C2 | semidirect |
| 5. #895 | C2 | semidirect |
| 6. #894 | C2 | semidirect |
| 7. #893 | C2 | semidirect |
| 8. #885 | C2 | semidirect |
| 9. #884 | C2 | semidirect |
| 10. #883 | C2 | semidirect |
| 11. #882 | C2 | semidirect |
| 12. #882 | C2 | semidirect |
| 13. D3×C22⋊C4 | C2 | semidirect |
| 14. #875 | C2 | semidirect |
| 15. C4×D12 | C2 | semidirect |
| 24. C2×D12 | C22 | semidirect |
| 27. C2×C4×D3 | C22 | semidirect |
| 28. C2×C4×D3 | C22 | semidirect |
| 29. C2×Dic6 | C22 | semidirect |
| 30. C3×C4⋊C4 | C22 | semidirect |
| 31. C3×C4⋊C4 | C22 | semidirect |
| 32. C3×C4⋊C4 | C22 | semidirect |
| 36. C3×C42 | C22 | semidirect |
| 44. (C2×D3)⋊C4 | C22 | semidirect |
| 45. (C2×D3)⋊C4 | C22 | semidirect |
| 46. (C2×D3)⋊C4 | C22 | semidirect |
| 47. (C2×D3)⋊C4 | C22 | semidirect |
| 48. C4⋊Dic3 | C22 | semidirect |
| 49. Dic3⋊C4 | C22 | semidirect |
| 50. Dic3⋊C4 | C22 | semidirect |
| 51. C4×Dic3 | C22 | semidirect |
| 53. #126 | D3 | semidirect |
| 113. C4⋊C4 | C2×D3 | semidirect |
| 114. C4⋊C4 | C2×D3 | semidirect |
| 115. C4⋊C4 | C2×D3 | semidirect |
| 131. C42 | C2×D3 | semidirect |
| 224. C3 | #538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#126 | 2 |
| #898 | 2 |
| #896 | 2 |
| #895 | 2 |
| #894 | 2 |
| #893 | 2 |
| #885 | 2 |
| #884 | 2 |
| #883 | 2 |
| #882 | 2 |
| D3×C22⋊C4 | 2 |
| #875 | 2 |
| C4×D12 | 2 |
| #538 | 3 |