Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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 | C2×C3×C22⋊C4 | C2 |
| hypercenter | C2×C22⋊C4 | D3 |
| hypocenter | C3 | #546 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#67 | C2 | semidirect |
| 2. C2×#235 | C2 | semidirect |
| 3. C2×C3×C22⋊C4 | C2 | semidirect |
| 4. #953 | C2 | semidirect |
| 5. #930 | C2 | semidirect |
| 6. #929 | C2 | semidirect |
| 7. C4×#67 | C2 | semidirect |
| 8. #885 | C2 | semidirect |
| 9. #884 | C2 | semidirect |
| 10. #884 | C2 | semidirect |
| 11. #883 | C2 | semidirect |
| 12. #882 | C2 | semidirect |
| 13. #67⋊C4 | C2 | semidirect |
| 14. D3×C22⋊C4 | C2 | semidirect |
| 15. #878 | C2 | semidirect |
| 19. C22×C3×C4 | C22 | semidirect |
| 20. C22×C3×C4 | C22 | semidirect |
| 27. C2×#67 | C22 | semidirect |
| 28. C2×#67 | C22 | semidirect |
| 31. C2×D12 | C22 | semidirect |
| 32. 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 |
| 39. C3×C22⋊C4 | C22 | semidirect |
| 40. C3×C22⋊C4 | C22 | semidirect |
| 42. #217 | C22 | semidirect |
| 43. #217 | 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. (C2×D3)⋊C4 | C22 | semidirect |
| 49. C4⋊Dic3 | C22 | semidirect |
| 50. Dic3⋊C4 | C22 | semidirect |
| 51. Dic3⋊C4 | C22 | semidirect |
| 52. Dic3⋊C4 | C22 | semidirect |
| 53. C4×Dic3 | C22 | semidirect |
| 68. C2×C22⋊C4 | D3 | semidirect |
| 93. #67 | D4 | semidirect |
| 124. C22×C4 | C2×D3 | semidirect |
| 125. C22×C4 | C2×D3 | semidirect |
| 140. C22⋊C4 | C2×D3 | semidirect |
| 141. C22⋊C4 | C2×D3 | semidirect |
| 152. C22×C3 | #41 | semidirect |
| 237. C22 | #235 | semidirect |
| 249. C3 | #546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67 | 2 |
| C2×#235 | 2 |
| C2×C3×C22⋊C4 | 2 |
| #953 | 2 |
| #930 | 2 |
| #929 | 2 |
| C4×#67 | 2 |
| #885 | 2 |
| #884 | 2 |
| #883 | 2 |
| #882 | 2 |
| #67⋊C4 | 2 |
| D3×C22⋊C4 | 2 |
| #878 | 2 |
| #546 | 3 |