Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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, prime radical | C3×#120 | C2 |
| hypercenter | #120 | D3 |
| hypocenter | C3 | #551 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#217 | C2 | semidirect |
| 3. #936 | C2 | semidirect |
| 4. #935 | C2 | semidirect |
| 5. #935 | C2 | semidirect |
| 6. D4×Dic3 | C2 | semidirect |
| 7. #879 | C2 | semidirect |
| 8. #878 | C2 | semidirect |
| 9. #877 | C2 | semidirect |
| 16. C22×Dic3 | C22 | semidirect |
| 17. C2×Dic6 | C22 | semidirect |
| 24. #217 | C22 | semidirect |
| 25. #217 | C22 | semidirect |
| 26. C4⋊Dic3 | C22 | semidirect |
| 27. Dic3⋊C4 | C22 | semidirect |
| 28. Dic3⋊C4 | C22 | semidirect |
| 29. Dic3⋊C4 | C22 | semidirect |
| 30. C4×Dic3 | C22 | semidirect |
| 31. C4×Dic3 | C22 | semidirect |
| 131. C3 | #551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#120 | 2 |
| C2×#217 | 2 |
| #936 | 2 |
| #935 | 2 |
| D4×Dic3 | 2 |
| #879 | 2 |
| #878 | 2 |
| #877 | 2 |
| #551 | 3 |