Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×C22⋊D83 |
| commutator, cosocle | C4×C83 | C25 |
| Frattini | C4 | C24×D83 |
| Fitting | #585×C83 | C2 |
| socle | C2×C83 | C23×D4 |
| hypercenter | #585 | D83 |
| hypocenter | C83 | #3586 |
| LCS | G ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14581839 | C2 | semidirect |
| 2. #19128516 | C2 | semidirect |
| 3. #19128512 | C2 | semidirect |
| 4. #19128499 | C2 | semidirect |
| 5. C2×#14581822 | C2 | semidirect |
| 6. #19128468 | C2 | semidirect |
| 7. #585×C83 | C2 | semidirect |
| 9. #14581839 | C22 | semidirect |
| 10. C2×#13050590 | C22 | semidirect |
| 12. C22×Dic166 | C22 | semidirect |
| 14. #14581823 | C22 | semidirect |
| 15. #14581822 | C22 | semidirect |
| 16. #14581822 | C22 | semidirect |
| 17. #14581818 | C22 | semidirect |
| 18. #14581817 | C22 | semidirect |
| 19. #14581812 | C22 | semidirect |
| 20. C2×#13050580 | C22 | semidirect |
| 21. C2×#13050578 | C22 | semidirect |
| 22. #14581799 | C22 | semidirect |
| 23. C2×#13050574 | C22 | semidirect |
| 25. 2−1+4×C83 | C22 | semidirect |
| 27. H(5,𝔽2)×C83 | C22 | semidirect |
| 113. C83 | #3586 | semidirect |
| 114. #585 | D83 | semidirect |
| 124. 2−1+4 | C2×D83 | semidirect |
| 126. H(5,𝔽2) | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581839 | 2 |
| #19128516 | 2 |
| #19128512 | 2 |
| #19128499 | 2 |
| C2×#14581822 | 2 |
| #19128468 | 2 |
| #585×C83 | 2 |
| #3586 | 83 |