Finite Group DatabasebetaFinite Group DatabasebetaOrder 5312.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 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×D83 |
| commutator, socle | C22×C83 | C24 |
| Fitting | #126×C83 | C2 |
| hypercenter | #126 | D83 |
| hypocenter | C83 | #542 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14581791 | C2 | semidirect |
| 2. #14581787 | C2 | semidirect |
| 3. #14581780 | C2 | semidirect |
| 4. #14581778 | C2 | semidirect |
| 5. #14581778 | C2 | semidirect |
| 6. #14581777 | C2 | semidirect |
| 7. #14581776 | C2 | semidirect |
| 8. #14581772 | C2 | semidirect |
| 9. #14581770 | C2 | semidirect |
| 10. #14581769 | C2 | semidirect |
| 12. C4×Dic166 | C2 | semidirect |
| 13. (C22⋊D83)⋊C4 | C2 | semidirect |
| 14. #14581750 | C2 | semidirect |
| 15. #126×C83 | C2 | semidirect |
| 103. C83 | #542 | semidirect |
| 107. #126 | D83 | semidirect |