Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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. #27161846 | C2 | semidirect |
| 3. #27161097 | C2 | semidirect |
| 4. #27160838 | C2 | semidirect |
| 5. #410×C197 | C2 | semidirect |
| 10. #20263324 | C4 | semidirect |
| 11. #20263322 | C4 | semidirect |
| 12. #20263315 | C4 | semidirect |
| 13. #20263313 | C4 | semidirect |
| 31. #15691342 | D4 | semidirect |
| 95. C197 | #1884 | semidirect |
| 100. #410 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161846 | 2 |
| #27161625 | 2 |
| #27161097 | 2 |
| #27160838 | 2 |
| #410×C197 | 2 |
| #1884 | 197 |