Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. #27163102 | C2 | semidirect |
| 3. #27163031 | C2 | semidirect |
| 4. #27163023 | C2 | semidirect |
| 5. #27163022 | C2 | semidirect |
| 6. #27163006 | C2 | semidirect |
| 7. #131×C397 | C2 | semidirect |
| 9. #20263721 | C4 | semidirect |
| 10. #20263719 | C4 | semidirect |
| 11. #20263718 | C4 | semidirect |
| 12. #20263716 | C4 | semidirect |
| 51. C397 | #444 | semidirect |
| 55. #131 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163116 | 2 |
| #27163102 | 2 |
| #27163031 | 2 |
| #27163023 | 2 |
| #27163022 | 2 |
| #27163006 | 2 |
| #131×C397 | 2 |
| #444 | 397 |