Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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×D97 |
| commutator, socle | C22×C97 | C24 |
| Fitting | #121×C97 | C2 |
| hypercenter | #121 | D97 |
| hypocenter | C97 | #560 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15690806 | C2 | semidirect |
| 2. #15690805 | C2 | semidirect |
| 3. #15690803 | C2 | semidirect |
| 4. #15690795 | C2 | semidirect |
| 5. #15690794 | C2 | semidirect |
| 6. #15690793 | C2 | semidirect |
| 7. #15690784 | C2 | semidirect |
| 8. #15690783 | C2 | semidirect |
| 9. #15690782 | C2 | semidirect |
| 10. #15690782 | C2 | semidirect |
| 11. #15690781 | C2 | semidirect |
| 12. #15690780 | C2 | semidirect |
| 13. #15690778 | C2 | semidirect |
| 14. #15690778 | C2 | semidirect |
| 15. #121×C97 | C2 | semidirect |
| 24. C2×C22⋊D97 | C22 | semidirect |
| 25. C2×C22⋊D97 | C22 | semidirect |
| 26. C22×Dic97 | C22 | semidirect |
| 27. C2×C4×D97 | C22 | semidirect |
| 28. C4⋊Dic97 | C22 | semidirect |
| 29. C4⋊Dic97 | C22 | semidirect |
| 30. #13095490 | C22 | semidirect |
| 31. #13095490 | C22 | semidirect |
| 32. #13095490 | C22 | semidirect |
| 35. C22⋊Dic97 | C22 | semidirect |
| 42. #13095488 | C22 | semidirect |
| 43. C4×Dic97 | C22 | semidirect |
| 46. C2×D4×C97 | C22 | semidirect |
| 47. C22×C4×C97 | C22 | semidirect |
| 48. C4⋊C4×C97 | C22 | semidirect |
| 50. C22⋊C4×C97 | C22 | semidirect |
| 122. C97 | #560 | semidirect |
| 135. #121 | D97 | semidirect |
| 151. C2×D4 | C2×D97 | semidirect |
| 154. C22×C4 | C2×D97 | semidirect |
| 160. C4⋊C4 | C2×D97 | semidirect |
| 172. C22⋊C4 | C2×D97 | semidirect |