Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #560 |
| 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. C3×#123 | C2 | semidirect |
| 2. #940 | C2 | semidirect |
| 3. #937 | C2 | semidirect |
| 4. #930 | C2 | semidirect |
| 5. #898 | C2 | semidirect |
| 6. #895 | C2 | semidirect |
| 7. #884 | C2 | semidirect |
| 8. #883 | C2 | semidirect |
| 9. #882 | C2 | semidirect |
| 13. C22×C3×C4 | C22 | semidirect |
| 16. C2×#67 | C22 | semidirect |
| 19. C2×D12 | C22 | semidirect |
| 20. C2×C4×D3 | C22 | semidirect |
| 21. C3×C4⋊C4 | C22 | semidirect |
| 23. C3×C22⋊C4 | C22 | semidirect |
| 28. (C2×D3)⋊C4 | C22 | semidirect |
| 29. C4⋊Dic3 | C22 | semidirect |
| 30. Dic3⋊C4 | C22 | semidirect |
| 31. C4×Dic3 | C22 | semidirect |
| 35. #123 | D3 | semidirect |
| 70. C22×C4 | C2×D3 | semidirect |
| 73. C4⋊C4 | C2×D3 | semidirect |
| 80. C22⋊C4 | C2×D3 | semidirect |
| 142. C3 | #560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#123 | 2 |
| #940 | 2 |
| #937 | 2 |
| #930 | 2 |
| #898 | 2 |
| #895 | 2 |
| #884 | 2 |
| #883 | 2 |
| #882 | 2 |
| #560 | 3 |