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×#117 | C2 |
| prime radical | #930 | C2 |
| hypercenter | #117 | D3 |
| hypocenter | C3 | #542 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#117 | C2 | semidirect |
| 3. #924 | C2 | semidirect |
| 4. #898 | C2 | semidirect |
| 5. #896 | C2 | semidirect |
| 6. #885 | C2 | semidirect |
| 7. #883 | C2 | semidirect |
| 8. #875 | C2 | semidirect |
| 9. C4×D12 | C2 | semidirect |
| 10. #869 | C2 | semidirect |
| 11. C4×Dic6 | C2 | semidirect |
| 46. #117 | 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×#117 | 2 |
| #930 | 2 |
| #924 | 2 |
| #898 | 2 |
| #896 | 2 |
| #885 | 2 |
| #883 | 2 |
| #875 | 2 |
| C4×D12 | 2 |
| #869 | 2 |
| C4×Dic6 | 2 |
| #542 | 3 |