Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Frattini | C22 | C23×D3 |
| Fitting | C3×C4×D4 | C2 |
| prime radical | #939 | C2 |
| hypercenter | C4×D4 | D3 |
| hypocenter | C3 | #529 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C4×D4 | C2 | semidirect |
| 3. #935 | C2 | semidirect |
| 4. C4×#67 | C2 | semidirect |
| 5. C4×#67 | C2 | semidirect |
| 6. #926 | C2 | semidirect |
| 7. C2×C4×Dic3 | C2 | semidirect |
| 8. #898 | C2 | semidirect |
| 9. #889 | C2 | semidirect |
| 10. #886 | C2 | semidirect |
| 11. #885 | C2 | semidirect |
| 12. #879 | C2 | semidirect |
| 13. #878 | C2 | semidirect |
| 14. #872 | C2 | semidirect |
| 15. C4×Dic6 | C2 | semidirect |
| 63. C4×D4 | D3 | semidirect |
| 200. C3 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D4 | 2 |
| #939 | 2 |
| #935 | 2 |
| C4×#67 | 2 |
| #926 | 2 |
| C2×C4×Dic3 | 2 |
| #898 | 2 |
| #889 | 2 |
| #886 | 2 |
| #885 | 2 |
| #879 | 2 |
| #878 | 2 |
| #872 | 2 |
| C4×Dic6 | 2 |
| #529 | 3 |