Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
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×D541 |
| commutator, socle, cosocle | C22×C541 | C24 |
| Fitting | #126×C541 | C2 |
| prime radical | #31772601 | C2 |
| hypercenter | #126 | D541 |
| hypocenter | C541 | #539 |
| LCS | G ▷ C22×C541 ▷ C541 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31772623 | C2 | semidirect |
| 2. #31772620 | C2 | semidirect |
| 3. #31772619 | C2 | semidirect |
| 4. #31772613 | C2 | semidirect |
| 5. #31772612 | C2 | semidirect |
| 6. #31772610 | C2 | semidirect |
| 7. #31772610 | C2 | semidirect |
| 8. #31772608 | C2 | semidirect |
| 9. #31772606 | C2 | semidirect |
| 10. #31772605 | C2 | semidirect |
| 12. C4×D2164 | C2 | semidirect |
| 13. #31772588 | C2 | semidirect |
| 14. C4⋊C4×D541 | C2 | semidirect |
| 15. #126×C541 | C2 | semidirect |
| 103. C541 | #539 | semidirect |
| 106. #126 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772623 | 2 |
| #31772620 | 2 |
| #31772619 | 2 |
| #31772613 | 2 |
| #31772612 | 2 |
| #31772610 | 2 |
| #31772608 | 2 |
| #31772606 | 2 |
| #31772605 | 2 |
| #31772601 | 2 |
| C4×D2164 | 2 |
| #31772588 | 2 |
| C4⋊C4×D541 | 2 |
| #126×C541 | 2 |
| #539 | 541 |