Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #939 | C2 |
| hypercenter | #123 | D3 |
| hypocenter | C3 | #542 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#123 | C2 | semidirect |
| 3. #936 | C2 | semidirect |
| 4. C4×#67 | C2 | semidirect |
| 5. #924 | C2 | semidirect |
| 6. #898 | C2 | semidirect |
| 7. #896 | C2 | semidirect |
| 8. #888 | C2 | semidirect |
| 9. #887 | C2 | semidirect |
| 10. #885 | C2 | semidirect |
| 11. #885 | C2 | semidirect |
| 12. #883 | C2 | semidirect |
| 13. #879 | C2 | semidirect |
| 14. #878 | C2 | semidirect |
| 15. #877 | C2 | semidirect |
| 59. #123 | D3 | semidirect |
| 200. C3 | #542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#123 | 2 |
| #939 | 2 |
| #936 | 2 |
| C4×#67 | 2 |
| #924 | 2 |
| #898 | 2 |
| #896 | 2 |
| #888 | 2 |
| #887 | 2 |
| #885 | 2 |
| #883 | 2 |
| #879 | 2 |
| #878 | 2 |
| #877 | 2 |
| #542 | 3 |