Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
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×D109 |
| commutator, socle | C22×C109 | C24 |
| Fitting | #117×C109 | C2 |
| hypercenter | #117 | D109 |
| hypocenter | C109 | #551 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16812694 | C2 | semidirect |
| 2. #16812693 | C2 | semidirect |
| 3. #16812687 | C2 | semidirect |
| 4. #16812684 | C2 | semidirect |
| 5. #16812684 | C2 | semidirect |
| 6. #16812682 | C2 | semidirect |
| 7. #16812677 | C2 | semidirect |
| 8. #16812676 | C2 | semidirect |
| 10. C4×D436 | C2 | semidirect |
| 11. #16812659 | C2 | semidirect |
| 12. #16812656 | C2 | semidirect |
| 13. C2×#13182006 | C2 | semidirect |
| 14. C22⋊C4×D109 | C2 | semidirect |
| 15. #117×C109 | C2 | semidirect |
| 17. C2×Dic218 | C22 | semidirect |
| 24. C2×C4×D109 | C22 | semidirect |
| 25. C4⋊Dic109 | C22 | semidirect |
| 26. #13182008 | C22 | semidirect |
| 27. #13182008 | C22 | semidirect |
| 28. #13182008 | C22 | semidirect |
| 29. #13182008 | C22 | semidirect |
| 30. #13182008 | C22 | semidirect |
| 40. #13182006 | C22 | semidirect |
| 41. #13182006 | C22 | semidirect |
| 42. #13182006 | C22 | semidirect |
| 43. C4×Dic109 | C22 | semidirect |
| 45. C4⋊C4×C109 | C22 | semidirect |
| 46. C4⋊C4×C109 | C22 | semidirect |
| 49. C42×C109 | C22 | semidirect |
| 50. C42×C109 | C22 | semidirect |
| 110. C109 | #551 | semidirect |
| 124. #117 | D109 | semidirect |
| 143. C4⋊C4 | C2×D109 | semidirect |
| 144. C4⋊C4 | C2×D109 | semidirect |
| 160. C42 | C2×D109 | semidirect |
| 161. C42 | C2×D109 | semidirect |