Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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×D97 |
| commutator, socle | C22×C97 | C24 |
| Fitting | #126×C97 | C2 |
| hypercenter | #126 | D97 |
| hypocenter | C97 | #560 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15690807 | C2 | semidirect |
| 2. #15690804 | C2 | semidirect |
| 3. #15690795 | C2 | semidirect |
| 4. #15690785 | C2 | semidirect |
| 5. #15690783 | C2 | semidirect |
| 6. #15690780 | C2 | semidirect |
| 7. #126×C97 | C2 | semidirect |
| 11. C2×D388 | C22 | semidirect |
| 13. C2×C4×D97 | C22 | semidirect |
| 14. #13095490 | C22 | semidirect |
| 17. #13095488 | C22 | semidirect |
| 18. C4⋊C4×C97 | C22 | semidirect |
| 20. C42×C97 | C22 | semidirect |
| 50. C97 | #560 | semidirect |
| 54. #126 | D97 | semidirect |
| 66. C4⋊C4 | C2×D97 | semidirect |
| 71. C42 | C2×D97 | semidirect |