Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#15691347 | C2 | semidirect |
| 3. C2×#20263313 | C2 | semidirect |
| 4. C2×#20263288 | C2 | semidirect |
| 5. #27161293 | C2 | direct (N × H) |
| 6. C2×#20263255 | C2 | semidirect |
| 7. C2×#20263249 | C2 | semidirect |
| 8. C2×#102×C197 | C2 | semidirect |
| 13. C2×#15691347 | C22 | semidirect |
| 18. #20263313 | C22 | semidirect |
| 20. #20263288 | C22 | semidirect |
| 25. #20263255 | C22 | semidirect |
| 26. #20263249 | C22 | semidirect |
| 30. #102×C197 | C22 | semidirect |
| 118. C2×C197 | #463 | semidirect |
| 123. C197 | C2×#463 | semidirect |
| 132. C2×#102 | D197 | semidirect |
| 154. #102 | C2×D197 | semidirect |
| 243. C2 | #27161293 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691347 | 2 |
| C22×#15691343 | 2 |
| C2×#20263313 | 2 |
| C2×#20263288 | 2 |
| #27161293 | 2 |
| C2×#20263255 | 2 |
| C2×#20263249 | 2 |
| C2×#102×C197 | 2 |
| C2×#463 | 197 |