Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 218 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×D547 |
| commutator, socle, cosocle | C22×C547 | C24 |
| Fitting | #126×C547 | C2 |
| prime radical | #31775975 | C2 |
| hypercenter | #126 | D547 |
| hypocenter | C547 | #539 |
| LCS | G ▷ C22×C547 ▷ C547 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31775997 | C2 | semidirect |
| 2. #31775994 | C2 | semidirect |
| 3. #31775993 | C2 | semidirect |
| 4. #31775987 | C2 | semidirect |
| 5. #31775986 | C2 | semidirect |
| 6. #31775984 | C2 | semidirect |
| 7. #31775984 | C2 | semidirect |
| 8. #31775982 | C2 | semidirect |
| 9. #31775980 | C2 | semidirect |
| 10. #31775979 | C2 | semidirect |
| 12. C4×D2188 | C2 | semidirect |
| 13. (C22⋊D547)⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D547 | C2 | semidirect |
| 15. #126×C547 | C2 | semidirect |
| 103. C547 | #539 | semidirect |
| 106. #126 | D547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31775997 | 2 |
| #31775994 | 2 |
| #31775993 | 2 |
| #31775987 | 2 |
| #31775986 | 2 |
| #31775984 | 2 |
| #31775982 | 2 |
| #31775980 | 2 |
| #31775979 | 2 |
| #31775975 | 2 |
| C4×D2188 | 2 |
| (C22⋊D547)⋊C4 | 2 |
| C4⋊C4×D547 | 2 |
| #126×C547 | 2 |
| #539 | 547 |