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 | C22⋊Q8×C109 | C2 |
| hypercenter | C22⋊Q8 | D109 |
| hypocenter | C109 | #551 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16812694 | C2 | semidirect |
| 2. #16812694 | C2 | semidirect |
| 3. #16812688 | C2 | semidirect |
| 4. #16812684 | C2 | semidirect |
| 5. #16812684 | C2 | semidirect |
| 6. #16812683 | C2 | semidirect |
| 7. #16812675 | C2 | semidirect |
| 9. #16812661 | C2 | semidirect |
| 10. C4×C22⋊D109 | C2 | semidirect |
| 11. #16812657 | C2 | semidirect |
| 12. #16812655 | C2 | semidirect |
| 13. C2×#13182006 | C2 | semidirect |
| 14. C22⋊C4×D109 | C2 | semidirect |
| 15. C22⋊Q8×C109 | C2 | semidirect |
| 23. C2×C4×D109 | C22 | semidirect |
| 24. C4⋊Dic109 | C22 | semidirect |
| 25. C4⋊Dic109 | C22 | semidirect |
| 26. #13182008 | C22 | semidirect |
| 27. #13182008 | C22 | semidirect |
| 28. #13182008 | C22 | semidirect |
| 38. #13182006 | C22 | semidirect |
| 39. #13182006 | C22 | semidirect |
| 40. #13182006 | C22 | semidirect |
| 41. C4×Dic109 | C22 | semidirect |
| 42. C4×Dic109 | C22 | semidirect |
| 43. C4×Dic109 | C22 | semidirect |
| 44. C2×Q8×C109 | C22 | semidirect |
| 46. C4⋊C4×C109 | C22 | semidirect |
| 47. C4⋊C4×C109 | C22 | semidirect |
| 48. C4⋊C4×C109 | C22 | semidirect |
| 110. C109 | #551 | semidirect |
| 119. C22⋊Q8 | D109 | semidirect |
| 128. C2×Q8 | C2×D109 | semidirect |
| 142. C4⋊C4 | C2×D109 | semidirect |
| 143. C4⋊C4 | C2×D109 | semidirect |
| 144. C4⋊C4 | C2×D109 | semidirect |