Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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×#15691357 | C2 | semidirect |
| 2. #27161627 | C2 | direct (N × H) |
| 3. C2×#20263326 | C2 | semidirect |
| 4. C2×#20263313 | C2 | semidirect |
| 5. C2×#20263297 | C2 | semidirect |
| 6. C2×D4×Dic197 | C2 | semidirect |
| 7. C2×C42×D197 | C2 | semidirect |
| 8. C2×#127×C197 | C2 | semidirect |
| 10. C2×#15691357 | C22 | semidirect |
| 16. #20263326 | C22 | semidirect |
| 17. #20263313 | C22 | semidirect |
| 18. #20263297 | C22 | semidirect |
| 19. D4×Dic197 | C22 | semidirect |
| 24. C42×D197 | C22 | semidirect |
| 27. #127×C197 | C22 | semidirect |
| 41. C2×C4×D197 | D4 | semidirect |
| 69. C4×D197 | C2×D4 | semidirect |
| 77. C2×C4×C197 | #41 | semidirect |
| 90. C4×C197 | C2×#41 | semidirect |
| 95. C2×C197 | #532 | semidirect |
| 99. C197 | C2×#532 | semidirect |
| 104. C2×#127 | D197 | semidirect |
| 119. #127 | C2×D197 | semidirect |
| 177. C2×C4 | #15691357 | semidirect |
| 193. C4 | C2×#15691357 | semidirect |
| 196. C2 | #27161627 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691357 | 2 |
| #27161627 | 2 |
| C2×#20263326 | 2 |
| C2×#20263313 | 2 |
| C2×#20263297 | 2 |
| C2×D4×Dic197 | 2 |
| C2×C42×D197 | 2 |
| C2×#127×C197 | 2 |
| C2×#532 | 197 |