Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
258 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C3×C4 | C24 |
| commutator | C2 | C23×C3×C4 |
| Frattini, cosocle | C4 | C24×C3 |
| socle | C2×C3 | C23×C4 |
| prime radical | C2×C3×#41 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#131 | C2 | semidirect |
| 3. C2×C3×M16 | C2 | semidirect |
| 4. #568 | C3 | direct (N × H) |
| 11. C3×M16 | C22 | semidirect |
| 12. C2×C3×C8 | C22 | semidirect |
| 14. #131 | C2×C3 | semidirect |
| 15. C2×M16 | C2×C3 | semidirect |
| 30. M16 | C22×C3 | semidirect |
| 31. C2×C8 | C22×C3 | semidirect |
| 55. C3 | #568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41 | 2 |
| C3×#131 | 2 |
| C2×C3×M16 | 2 |
| #568 | 3 |