Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27161636 | C2 | semidirect |
| 2. #27161438 | C2 | semidirect |
| 3. #27161433 | C2 | semidirect |
| 4. #27161088 | C2 | semidirect |
| 6. C4×#15691342 | C2 | semidirect |
| 9. #20263326 | C22 | semidirect |
| 10. #20263318 | C22 | semidirect |
| 14. #20263250 | C22 | semidirect |
| 16. #20263237 | C22 | semidirect |
| 17. C4×#13096802 | C22 | semidirect |
| 83. C197 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161636 | 2 |
| #27161438 | 2 |
| #27161433 | 2 |
| #27161088 | 2 |
| #27161084 | 2 |
| C4×#15691342 | 2 |
| C2×#124×C197 | 2 |
| #3140 | 197 |