Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D109 |
| commutator | C4×C109 | C24 |
| Frattini | C4 | C23×D109 |
| Fitting | C2×D8×C109 | C2 |
| socle | C2×C109 | C22×D4 |
| hypercenter | C2×D8 | D109 |
| hypocenter | C109 | #576 |
| LCS | G ▷ C4×C109 ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16812744 | C2 | semidirect |
| 2. #16812725 | C2 | semidirect |
| 3. #16812723 | C2 | semidirect |
| 4. #16812721 | C2 | semidirect |
| 5. #16812718 | C2 | semidirect |
| 6. D8×D109 | C2 | semidirect |
| 7. #16812705 | C2 | semidirect |
| 8. C2×D8×C109 | C2 | semidirect |
| 10. #13182029 | C22 | semidirect |
| 12. #13182028 | C22 | semidirect |
| 15. D4×D109 | C22 | semidirect |
| 16. Dic436 | C22 | semidirect |
| 17. #13182018 | C22 | semidirect |
| 18. #13182017 | C22 | semidirect |
| 19. D872 | C22 | semidirect |
| 20. #13182014 | C22 | semidirect |
| 21. #13182013 | C22 | semidirect |
| 22. #13182012 | C22 | semidirect |
| 23. C8×D109 | C22 | semidirect |
| 24. C2×D4×C109 | C22 | semidirect |
| 25. D8×C109 | C22 | semidirect |
| 26. D8×C109 | C22 | semidirect |
| 27. C2×C8×C109 | C22 | semidirect |
| 62. C109 | #576 | semidirect |
| 70. C2×D8 | D109 | semidirect |
| 79. C2×D4 | C2×D109 | semidirect |
| 85. D8 | C2×D109 | semidirect |
| 86. D8 | C2×D109 | semidirect |
| 90. C2×C8 | C2×D109 | semidirect |