Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #27163089 | C2 | semidirect |
| 2. #27163089 | C2 | semidirect |
| 3. #27163082 | C2 | semidirect |
| 4. #27163080 | C2 | semidirect |
| 5. #27163079 | C2 | semidirect |
| 6. #27163078 | C2 | semidirect |
| 7. #27163075 | C2 | semidirect |
| 8. #27163073 | C2 | semidirect |
| 10. C4×C22⋊D397 | C2 | semidirect |
| 11. #27163056 | C2 | semidirect |
| 12. #27163055 | C2 | semidirect |
| 13. #27163052 | C2 | semidirect |
| 14. C2×C22⋊Dic397 | C2 | semidirect |
| 15. C2×C22⋊C4×C397 | C2 | semidirect |
| 16. C2×Dic794 | C22 | semidirect |
| 22. C2×C4×D397 | C22 | semidirect |
| 23. C4⋊Dic397 | C22 | semidirect |
| 24. C4⋊Dic397 | C22 | semidirect |
| 25. C4⋊Dic397 | C22 | semidirect |
| 26. #20263710 | C22 | semidirect |
| 27. #20263710 | C22 | semidirect |
| 28. #20263710 | C22 | semidirect |
| 29. #20263710 | C22 | semidirect |
| 30. #20263710 | C22 | semidirect |
| 38. #20263708 | C22 | semidirect |
| 39. #20263708 | C22 | semidirect |
| 40. #20263708 | C22 | semidirect |
| 41. C4×Dic397 | C22 | semidirect |
| 42. C4×Dic397 | C22 | semidirect |
| 43. C4×Dic397 | C22 | semidirect |
| 110. C397 | #551 | semidirect |
| 126. C2×C22⋊C4 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163089 | 2 |
| #27163082 | 2 |
| #27163080 | 2 |
| #27163079 | 2 |
| #27163078 | 2 |
| #27163075 | 2 |
| #27163073 | 2 |
| #27163065 | 2 |
| C4×C22⋊D397 | 2 |
| #27163056 | 2 |
| #27163055 | 2 |
| #27163052 | 2 |
| C2×C22⋊Dic397 | 2 |
| C2×C22⋊C4×C397 | 2 |
| #551 | 397 |