Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27163091 | C2 | semidirect |
| 2. #27163089 | C2 | semidirect |
| 3. #27163086 | C2 | semidirect |
| 4. #27163082 | C2 | semidirect |
| 5. #27163080 | C2 | semidirect |
| 6. #27163077 | C2 | semidirect |
| 7. #27163073 | C2 | semidirect |
| 9. C4×Dic794 | C2 | semidirect |
| 10. C4×C22⋊D397 | C2 | semidirect |
| 11. C4×C22⋊D397 | C2 | semidirect |
| 12. #27163055 | C2 | semidirect |
| 13. #27163053 | C2 | semidirect |
| 14. C2×C4×Dic397 | C2 | semidirect |
| 15. C4×D4×C397 | C2 | semidirect |
| 103. C397 | #529 | semidirect |
| 116. C4×D4 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163091 | 2 |
| #27163089 | 2 |
| #27163086 | 2 |
| #27163082 | 2 |
| #27163080 | 2 |
| #27163077 | 2 |
| #27163073 | 2 |
| #27163068 | 2 |
| C4×Dic794 | 2 |
| C4×C22⋊D397 | 2 |
| #27163055 | 2 |
| #27163053 | 2 |
| C2×C4×Dic397 | 2 |
| C4×D4×C397 | 2 |
| #529 | 397 |