Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 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×#15691345 | C2 | semidirect |
| 2. C22×C8×D197 | C2 | semidirect |
| 3. C2×#20263302 | C2 | semidirect |
| 5. #27161311 | C2 | direct (N × H) |
| 6. C2×#20263257 | C2 | semidirect |
| 7. C2×#20263248 | C2 | semidirect |
| 8. C2×#103×C197 | C2 | semidirect |
| 13. C2×#15691345 | C22 | semidirect |
| 16. C2×C8×D197 | C22 | semidirect |
| 18. #20263302 | C22 | semidirect |
| 25. #20263257 | C22 | semidirect |
| 26. #20263248 | C22 | semidirect |
| 30. #103×C197 | C22 | semidirect |
| 46. C2×#13096802 | D4 | semidirect |
| 71. C22×D197 | SD16 | semidirect |
| 84. #13096802 | C2×D4 | semidirect |
| 109. C2×D197 | C2×SD16 | semidirect |
| 117. C2×C197 | #465 | semidirect |
| 123. C197 | C2×#465 | semidirect |
| 131. C2×#103 | D197 | semidirect |
| 153. #103 | C2×D197 | semidirect |
| 243. C2 | #27161311 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691345 | 2 |
| C22×C8×D197 | 2 |
| C2×#20263302 | 2 |
| C2×#20263301 | 2 |
| #27161311 | 2 |
| C2×#20263257 | 2 |
| C2×#20263248 | 2 |
| C2×#103×C197 | 2 |
| C2×#465 | 197 |