Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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×#124 | C2 |
| prime radical | #938 | C2 |
| hypercenter | #124 | D3 |
| hypocenter | C3 | #542 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#124 | C2 | semidirect |
| 2. #946 | C2 | semidirect |
| 3. Q8×Dic3 | C2 | semidirect |
| 5. D4×Dic3 | C2 | semidirect |
| 6. #886 | C2 | semidirect |
| 7. #885 | C2 | semidirect |
| 8. #879 | C2 | semidirect |
| 9. #878 | C2 | semidirect |
| 10. #872 | C2 | semidirect |
| 11. #869 | C2 | semidirect |
| 39. #124 | D3 | semidirect |
| 141. C3 | #542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#124 | 2 |
| #946 | 2 |
| Q8×Dic3 | 2 |
| #938 | 2 |
| D4×Dic3 | 2 |
| #886 | 2 |
| #885 | 2 |
| #879 | 2 |
| #878 | 2 |
| #872 | 2 |
| #869 | 2 |
| #542 | 3 |