Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #27161692 | C2 | direct (N × H) |
| 2. C2×#20263326 | C2 | semidirect |
| 4. C2×#20263317 | C2 | semidirect |
| 6. C2×#20263291 | C2 | semidirect |
| 8. C2×#125×C197 | C2 | semidirect |
| 11. #20263326 | C22 | semidirect |
| 13. #20263317 | C22 | semidirect |
| 15. #20263291 | C22 | semidirect |
| 25. #125×C197 | C22 | semidirect |
| 81. C2×C197 | #541 | semidirect |
| 85. C197 | C2×#541 | semidirect |
| 91. C2×#125 | D197 | semidirect |
| 100. #125 | C2×D197 | semidirect |
| 168. C2 | #27161692 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161692 | 2 |
| C2×#20263326 | 2 |
| C2×#20263321 | 2 |
| C2×#20263317 | 2 |
| C2×#20263306 | 2 |
| C2×#20263291 | 2 |
| C2×#20263283 | 2 |
| C2×#125×C197 | 2 |
| C2×#541 | 197 |