Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×D109 |
| commutator, socle | C22×C109 | C24 |
| Fitting | #120×C109 | C2 |
| hypercenter | #120 | D109 |
| hypocenter | C109 | #535 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13182028 | C2 | semidirect |
| 2. C22×C22⋊D109 | C2 | semidirect |
| 3. #16812695 | C2 | semidirect |
| 4. #16812685 | C2 | semidirect |
| 5. #16812672 | C2 | semidirect |
| 6. #16812671 | C2 | semidirect |
| 7. #16812669 | C2 | semidirect |
| 8. #16812668 | C2 | semidirect |
| 9. #16812667 | C2 | semidirect |
| 10. #16812655 | C2 | semidirect |
| 11. #120×C109 | C2 | semidirect |
| 14. C2×Dic218 | C22 | semidirect |
| 15. C2×D436 | C22 | semidirect |
| 20. C2×C22⋊D109 | C22 | semidirect |
| 21. C2×C22⋊D109 | C22 | semidirect |
| 22. C2×C22⋊D109 | C22 | semidirect |
| 24. C22×Dic109 | C22 | semidirect |
| 25. C2×C4×D109 | C22 | semidirect |
| 26. #13182008 | C22 | semidirect |
| 28. C22⋊Dic109 | C22 | semidirect |
| 29. #13182006 | C22 | semidirect |
| 30. #13182006 | C22 | semidirect |
| 31. C4×Dic109 | C22 | semidirect |
| 34. C2×D4×C109 | C22 | semidirect |
| 36. C22⋊C4×C109 | C22 | semidirect |
| 57. C2×Dic109 | D4 | semidirect |
| 93. C109 | #535 | semidirect |
| 104. #120 | D109 | semidirect |
| 119. C2×D4 | C2×D109 | semidirect |
| 129. C22⋊C4 | C2×D109 | semidirect |