Finite Group DatabasebetaFinite Group DatabasebetaOrder 4672.
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×D73 |
| commutator, socle, cosocle | C22×C73 | C24 |
| Fitting | #124×C73 | C2 |
| prime radical | #14556563 | C2 |
| hypercenter | #124 | D73 |
| hypocenter | C73 | #542 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14556589 | C2 | semidirect |
| 2. #14556585 | C2 | semidirect |
| 3. #14556584 | C2 | semidirect |
| 4. #14556577 | C2 | semidirect |
| 5. #14556577 | C2 | semidirect |
| 6. #14556573 | C2 | semidirect |
| 7. #14556572 | C2 | semidirect |
| 8. #14556568 | C2 | semidirect |
| 9. #14556568 | C2 | semidirect |
| 10. #14556567 | C2 | semidirect |
| 12. C4×Dic146 | C2 | semidirect |
| 13. #14556551 | C2 | semidirect |
| 14. #14556547 | C2 | semidirect |
| 15. #124×C73 | C2 | semidirect |
| 103. C73 | #542 | semidirect |
| 110. #124 | D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14556589 | 2 |
| #14556585 | 2 |
| #14556584 | 2 |
| #14556577 | 2 |
| #14556573 | 2 |
| #14556572 | 2 |
| #14556568 | 2 |
| #14556567 | 2 |
| #14556563 | 2 |
| C4×Dic146 | 2 |
| #14556551 | 2 |
| #14556547 | 2 |
| #124×C73 | 2 |
| #542 | 73 |