Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #123×C97 | C2 |
| hypercenter | #123 | D97 |
| hypocenter | C97 | #525 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13095510 | C2 | semidirect |
| 2. C22×C4×D97 | C2 | semidirect |
| 3. #15690793 | C2 | semidirect |
| 4. #15690788 | C2 | semidirect |
| 5. #15690783 | C2 | semidirect |
| 6. #15690780 | C2 | semidirect |
| 7. #15690778 | C2 | semidirect |
| 8. #15690772 | C2 | semidirect |
| 9. #15690770 | C2 | semidirect |
| 10. #15690766 | C2 | semidirect |
| 11. #123×C97 | C2 | semidirect |
| 14. C2×Dic194 | C22 | semidirect |
| 18. C2×C22⋊D97 | C22 | semidirect |
| 20. C22×Dic97 | C22 | semidirect |
| 24. C2×C4×D97 | C22 | semidirect |
| 25. #13095490 | C22 | semidirect |
| 26. #13095490 | C22 | semidirect |
| 30. #13095488 | C22 | semidirect |
| 31. C4×Dic97 | C22 | semidirect |
| 34. C4⋊C4×C97 | C22 | semidirect |
| 36. C22⋊C4×C97 | C22 | semidirect |
| 52. C2×Dic97 | D4 | semidirect |
| 72. C2×D97 | #41 | semidirect |
| 86. C97 | #525 | semidirect |
| 91. #123 | D97 | semidirect |
| 116. C4⋊C4 | C2×D97 | semidirect |
| 122. C22⋊C4 | C2×D97 | semidirect |