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×#123 | C2 |
| prime radical | #937 | C2 |
| hypercenter | #123 | D3 |
| hypocenter | C3 | #551 |
| 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 |
| 3. #936 | C2 | semidirect |
| 4. C4×#67 | C2 | semidirect |
| 5. #896 | C2 | semidirect |
| 6. #892 | C2 | semidirect |
| 7. #883 | C2 | semidirect |
| 8. D3×C22⋊C4 | C2 | semidirect |
| 9. #879 | C2 | semidirect |
| 13. C22×C3×C4 | C22 | semidirect |
| 17. C2×Dic6 | C22 | semidirect |
| 18. C3×C4⋊C4 | C22 | semidirect |
| 20. C3×C22⋊C4 | C22 | semidirect |
| 23. #217 | C22 | semidirect |
| 27. C4⋊Dic3 | C22 | semidirect |
| 28. Dic3⋊C4 | C22 | semidirect |
| 29. Dic3⋊C4 | C22 | semidirect |
| 30. C4×Dic3 | C22 | semidirect |
| 31. C4×Dic3 | C22 | semidirect |
| 35. #123 | D3 | semidirect |
| 64. C22×C4 | C2×D3 | semidirect |
| 68. C4⋊C4 | C2×D3 | semidirect |
| 76. C22⋊C4 | C2×D3 | semidirect |
| 131. C3 | #551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#123 | 2 |
| #937 | 2 |
| #936 | 2 |
| C4×#67 | 2 |
| #896 | 2 |
| #892 | 2 |
| #883 | 2 |
| D3×C22⋊C4 | 2 |
| #879 | 2 |
| #551 | 3 |