Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
240 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #123×C97 | C2 |
| hypercenter | #123 | D97 |
| hypocenter | C97 | #540 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15690806 | C2 | semidirect |
| 2. #15690800 | C2 | semidirect |
| 3. #15690795 | C2 | semidirect |
| 4. #15690794 | C2 | semidirect |
| 5. #15690792 | C2 | semidirect |
| 6. #15690785 | C2 | semidirect |
| 7. #15690784 | C2 | semidirect |
| 8. #15690783 | C2 | semidirect |
| 9. #15690783 | C2 | semidirect |
| 10. #15690783 | C2 | semidirect |
| 11. #15690782 | C2 | semidirect |
| 12. C4×C22⋊D97 | C2 | semidirect |
| 13. #15690770 | C2 | semidirect |
| 14. #15690768 | C2 | semidirect |
| 15. #123×C97 | C2 | semidirect |
| 115. C97 | #540 | semidirect |
| 122. #123 | D97 | semidirect |