Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #551 |
| 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. #15690805 | C2 | semidirect |
| 2. #15690805 | C2 | semidirect |
| 3. #15690796 | C2 | semidirect |
| 4. #15690794 | C2 | semidirect |
| 5. #15690792 | C2 | semidirect |
| 6. #15690790 | C2 | semidirect |
| 7. #15690787 | C2 | semidirect |
| 9. D4×Dic97 | C2 | semidirect |
| 10. #15690770 | C2 | semidirect |
| 11. #15690769 | C2 | semidirect |
| 12. #15690768 | C2 | semidirect |
| 13. C2×#13095488 | C2 | semidirect |
| 14. C22⋊C4×D97 | C2 | semidirect |
| 15. #123×C97 | C2 | semidirect |
| 17. C2×Dic194 | C22 | semidirect |
| 21. C22×Dic97 | C22 | semidirect |
| 24. C4⋊Dic97 | C22 | semidirect |
| 25. C4⋊Dic97 | C22 | semidirect |
| 26. C4⋊Dic97 | C22 | semidirect |
| 27. C4⋊Dic97 | C22 | semidirect |
| 28. #13095490 | C22 | semidirect |
| 29. #13095490 | C22 | semidirect |
| 32. C22⋊Dic97 | C22 | semidirect |
| 41. C4×Dic97 | C22 | semidirect |
| 42. C4×Dic97 | C22 | semidirect |
| 43. C4×Dic97 | C22 | semidirect |
| 46. C4⋊C4×C97 | C22 | semidirect |
| 47. C4⋊C4×C97 | C22 | semidirect |
| 49. C22⋊C4×C97 | C22 | semidirect |
| 50. C22⋊C4×C97 | C22 | semidirect |
| 110. C97 | #551 | semidirect |
| 117. #123 | D97 | semidirect |
| 143. C4⋊C4 | C2×D97 | semidirect |
| 144. C4⋊C4 | C2×D97 | semidirect |
| 157. C22⋊C4 | C2×D97 | semidirect |
| 158. C22⋊C4 | C2×D97 | semidirect |