Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 | C2×#237 | C2 |
| hypercenter | #123 | D3 |
| hypocenter | C3 | #536 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic6 | C2 | semidirect |
| 3. C3×#123 | C2 | semidirect |
| 4. #935 | C2 | semidirect |
| 5. #929 | C2 | semidirect |
| 6. #896 | C2 | semidirect |
| 7. #888 | C2 | semidirect |
| 8. #886 | C2 | semidirect |
| 9. #885 | C2 | semidirect |
| 10. #878 | C2 | semidirect |
| 11. #877 | C2 | semidirect |
| 45. #123 | D3 | semidirect |
| 153. C3 | #536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#237 | 2 |
| C22×Dic6 | 2 |
| C3×#123 | 2 |
| #935 | 2 |
| #929 | 2 |
| #896 | 2 |
| #888 | 2 |
| #886 | 2 |
| #885 | 2 |
| #878 | 2 |
| #877 | 2 |
| #536 | 3 |