Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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 | C2×#67 | C22 |
| hypercenter | C22⋊Q8 | D3 |
| hypocenter | C3 | #556 |
| 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. #946 | C2 | semidirect |
| 3. Q8×Dic3 | C2 | semidirect |
| 5. #926 | C2 | semidirect |
| 6. #898 | C2 | semidirect |
| 7. #892 | C2 | semidirect |
| 8. #888 | C2 | semidirect |
| 9. #887 | C2 | semidirect |
| 11. #879 | C2 | semidirect |
| 41. C22⋊Q8 | D3 | semidirect |
| 139. C3 | #556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C22⋊Q8 | 2 |
| #946 | 2 |
| Q8×Dic3 | 2 |
| C4×#67 | 2 |
| #926 | 2 |
| #898 | 2 |
| #892 | 2 |
| #888 | 2 |
| #887 | 2 |
| #885 | 2 |
| #879 | 2 |
| #556 | 3 |