Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 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 | #137×C109 | C2 |
| socle | C2×C109 | C22×D4 |
| hypercenter | #137 | D109 |
| hypocenter | C109 | C2×#137 |
| LCS | G ▷ C4×C109 ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D109 | C2 | semidirect |
| 3. #16812732 | C2 | semidirect |
| 4. #16812731 | C2 | semidirect |
| 5. #16812730 | C2 | semidirect |
| 6. #16812729 | C2 | semidirect |
| 7. #16812728 | C2 | semidirect |
| 8. Q16×D109 | C2 | semidirect |
| 9. SD16×D109 | C2 | semidirect |
| 10. M16×D109 | C2 | semidirect |
| 11. #137×C109 | C2 | semidirect |
| 18. C2×Dic218 | C22 | semidirect |
| 23. Q8×D109 | C22 | semidirect |
| 29. Dic436 | C22 | semidirect |
| 30. #13182019 | C22 | semidirect |
| 31. #13182019 | C22 | semidirect |
| 32. #13182018 | C22 | semidirect |
| 33. #13182017 | C22 | semidirect |
| 34. #13182016 | C22 | semidirect |
| 35. #13182013 | C22 | semidirect |
| 36. #13182012 | C22 | semidirect |
| 39. C2×Q8×C109 | C22 | semidirect |
| 40. Q16×C109 | C22 | semidirect |
| 41. SD16×C109 | C22 | semidirect |
| 42. M16×C109 | C22 | semidirect |
| 98. D109 | #137 | direct (N × H) |
| 99. C109 | C2×#137 | semidirect |
| 108. #137 | D109 | direct (N × H) |
| 125. C2×Q8 | C2×D109 | semidirect |
| 134. Q16 | C2×D109 | semidirect |
| 138. SD16 | C2×D109 | semidirect |
| 141. M16 | C2×D109 | semidirect |