Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
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×D97 |
| commutator | C4×C97 | C24 |
| Frattini | C4 | C23×D97 |
| Fitting | #137×C97 | C2 |
| socle | C2×C97 | C22×D4 |
| hypercenter | #137 | D97 |
| hypocenter | C97 | C2×#137 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D97 | C2 | semidirect |
| 3. #15690843 | C2 | semidirect |
| 4. #15690842 | C2 | semidirect |
| 5. #15690841 | C2 | semidirect |
| 6. #15690840 | C2 | semidirect |
| 7. #15690839 | C2 | semidirect |
| 8. Q16×D97 | C2 | semidirect |
| 9. SD16×D97 | C2 | semidirect |
| 10. M16×D97 | C2 | semidirect |
| 11. #137×C97 | C2 | semidirect |
| 18. C2×Dic194 | C22 | semidirect |
| 23. Q8×D97 | C22 | semidirect |
| 29. Dic388 | C22 | semidirect |
| 30. #13095501 | C22 | semidirect |
| 31. #13095501 | C22 | semidirect |
| 32. #13095500 | C22 | semidirect |
| 33. #13095499 | C22 | semidirect |
| 34. #13095498 | C22 | semidirect |
| 35. #13095495 | C22 | semidirect |
| 36. #13095494 | C22 | semidirect |
| 39. C2×Q8×C97 | C22 | semidirect |
| 40. Q16×C97 | C22 | semidirect |
| 41. SD16×C97 | C22 | semidirect |
| 42. M16×C97 | C22 | semidirect |
| 98. D97 | #137 | direct (N × H) |
| 99. C97 | C2×#137 | semidirect |
| 108. #137 | D97 | direct (N × H) |
| 125. C2×Q8 | C2×D97 | semidirect |
| 134. Q16 | C2×D97 | semidirect |
| 138. SD16 | C2×D97 | semidirect |
| 141. M16 | C2×D97 | semidirect |