Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
342 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
| prime radical | C2×D3×D4 | C2 |
| hypercenter | #123 | D3 |
| hypocenter | C3 | C2×#123 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4×D3 | C2 | semidirect |
| 3. C3×#123 | C2 | semidirect |
| 4. #935 | C2 | semidirect |
| 5. #929 | C2 | semidirect |
| 6. #894 | C2 | semidirect |
| 7. D3×C4⋊C4 | C2 | semidirect |
| 8. #886 | C2 | semidirect |
| 9. #883 | C2 | semidirect |
| 10. D3×C22⋊C4 | C2 | semidirect |
| 11. D3×C22⋊C4 | C2 | semidirect |
| 16. C22×C3×C4 | C22 | semidirect |
| 19. C22×Dic3 | C22 | semidirect |
| 26. C2×C4×D3 | C22 | semidirect |
| 27. C3×C4⋊C4 | C22 | semidirect |
| 28. C3×C22⋊C4 | C22 | semidirect |
| 29. C3×C22⋊C4 | C22 | semidirect |
| 30. #217 | C22 | semidirect |
| 31. #217 | C22 | semidirect |
| 32. (C2×D3)⋊C4 | C22 | semidirect |
| 33. (C2×D3)⋊C4 | C22 | semidirect |
| 34. (C2×D3)⋊C4 | C22 | semidirect |
| 35. C4⋊Dic3 | C22 | semidirect |
| 36. Dic3⋊C4 | C22 | semidirect |
| 37. Dic3⋊C4 | C22 | semidirect |
| 45. #123 | D3 | direct (N × H) |
| 87. C22×C4 | C2×D3 | semidirect |
| 91. C4⋊C4 | C2×D3 | semidirect |
| 97. C22⋊C4 | C2×D3 | semidirect |
| 98. C22⋊C4 | C2×D3 | semidirect |
| 149. D3 | #123 | direct (N × H) |
| 169. C3 | C2×#123 | 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×#123 | 2 |
| #935 | 2 |
| #929 | 2 |
| #894 | 2 |
| D3×C4⋊C4 | 2 |
| #886 | 2 |
| #883 | 2 |
| D3×C22⋊C4 | 2 |
| C2×#123 | 3 |