Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
192 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 192 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×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C29×#125 | C2 |
| prime radical | C22×D29 | C23 |
| hypercenter | #125 | D29 |
| hypocenter | C29 | #541 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#125 | C2 | semidirect |
| 8. #11745252 | C2 | semidirect |
| 9. #11745251 | C2 | semidirect |
| 10. #11745251 | C2 | semidirect |
| 11. #11745251 | C2 | semidirect |
| 12. #11745250 | C2 | semidirect |
| 13. #11745249 | C2 | semidirect |
| 15. C4×Dic58 | C2 | semidirect |
| 101. #125 | D29 | semidirect |
| 107. C29 | #541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#125 | 2 |
| #11745260 | 2 |
| #11745258 | 2 |
| #11745254 | 2 |
| #11745252 | 2 |
| #11745251 | 2 |
| #11745250 | 2 |
| #11745249 | 2 |
| #11745238 | 2 |
| C4×Dic58 | 2 |
| #541 | 29 |