Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 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 | #563 |
| 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. #15690810 | C2 | semidirect |
| 2. #15690809 | C2 | semidirect |
| 3. #15690805 | C2 | semidirect |
| 4. #15690804 | C2 | semidirect |
| 5. #15690803 | C2 | semidirect |
| 6. #15690801 | C2 | semidirect |
| 7. #15690800 | C2 | semidirect |
| 11. #15690790 | C2 | semidirect |
| 12. #15690788 | C2 | semidirect |
| 13. #15690787 | C2 | semidirect |
| 14. #15690787 | C2 | semidirect |
| 15. #126×C97 | C2 | semidirect |
| 97. C97 | #563 | semidirect |
| 104. #126 | D97 | semidirect |