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, Frattini | C22 | C23×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Fitting | C3×C22⋊Q8 | C2 |
| prime radical | #930 | C2 |
| hypercenter | C22⋊Q8 | D3 |
| hypocenter | C3 | #529 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C22⋊Q8 | C2 | semidirect |
| 2. #947 | C2 | semidirect |
| 3. Q8×Dic3 | C2 | semidirect |
| 5. C2×C4×Dic3 | C2 | semidirect |
| 6. #898 | C2 | semidirect |
| 7. #893 | C2 | semidirect |
| 8. #892 | C2 | semidirect |
| 9. #890 | C2 | semidirect |
| 10. #886 | C2 | semidirect |
| 11. #67⋊C4 | C2 | semidirect |
| 40. C22⋊Q8 | D3 | semidirect |
| 143. C3 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C22⋊Q8 | 2 |
| #947 | 2 |
| Q8×Dic3 | 2 |
| #930 | 2 |
| C2×C4×Dic3 | 2 |
| #898 | 2 |
| #893 | 2 |
| #892 | 2 |
| #890 | 2 |
| #886 | 2 |
| #67⋊C4 | 2 |
| #529 | 3 |