Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15691341 | C2 | semidirect |
| 2. C2×#20263302 | C2 | semidirect |
| 4. #27161322 | C2 | direct (N × H) |
| 5. C2×#20263260 | C2 | semidirect |
| 6. C2×#20263250 | C2 | semidirect |
| 7. C2×#20263247 | C2 | semidirect |
| 8. C22×SD16×C197 | C2 | semidirect |
| 12. C2×#15691341 | C22 | semidirect |
| 15. #20263302 | C22 | semidirect |
| 23. #20263260 | C22 | semidirect |
| 24. #20263250 | C22 | semidirect |
| 25. #20263247 | C22 | semidirect |
| 29. C2×SD16×C197 | C22 | semidirect |
| 63. C2×C8×C197 | D4 | semidirect |
| 97. C8×C197 | C2×D4 | semidirect |
| 118. C2×C197 | #468 | semidirect |
| 123. C197 | C2×#468 | semidirect |
| 125. C22×SD16 | D197 | semidirect |
| 138. C2×SD16 | C2×D197 | semidirect |
| 180. C2×C8 | C22⋊D197 | semidirect |
| 221. C8 | C2×C22⋊D197 | semidirect |
| 243. C2 | #27161322 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691341 | 2 |
| C2×#20263302 | 2 |
| C2×#20263297 | 2 |
| #27161322 | 2 |
| C2×#20263260 | 2 |
| C2×#20263250 | 2 |
| C2×#20263247 | 2 |
| C22×SD16×C197 | 2 |
| C2×#468 | 197 |