Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
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×D397 |
| commutator, socle, cosocle | C22×C397 | C24 |
| Fitting | #123×C397 | C2 |
| prime radical | #27163067 | C2 |
| hypercenter | #123 | D397 |
| hypocenter | C397 | #539 |
| LCS | G ▷ C22×C397 ▷ C397 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27163089 | C2 | semidirect |
| 2. #27163089 | C2 | semidirect |
| 3. #27163087 | C2 | semidirect |
| 4. #27163086 | C2 | semidirect |
| 5. #27163078 | C2 | semidirect |
| 6. #27163078 | C2 | semidirect |
| 7. #27163077 | C2 | semidirect |
| 8. #27163075 | C2 | semidirect |
| 9. #27163074 | C2 | semidirect |
| 10. #27163073 | C2 | semidirect |
| 12. C4×C22⋊D397 | C2 | semidirect |
| 13. #27163056 | C2 | semidirect |
| 14. C4⋊C4×D397 | C2 | semidirect |
| 15. #123×C397 | C2 | semidirect |
| 103. C397 | #539 | semidirect |
| 112. #123 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163089 | 2 |
| #27163087 | 2 |
| #27163086 | 2 |
| #27163078 | 2 |
| #27163077 | 2 |
| #27163075 | 2 |
| #27163074 | 2 |
| #27163073 | 2 |
| #27163067 | 2 |
| C4×C22⋊D397 | 2 |
| #27163056 | 2 |
| C4⋊C4×D397 | 2 |
| #123×C397 | 2 |
| #539 | 397 |