Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
1160 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 309 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×C22⋊Dic197 | C2 | semidirect |
| 2. #27160959 | C2 | semidirect |
| 3. #27160942 | C2 | semidirect |
| 4. #27160935 | C2 | semidirect |
| 6. C23×Dic197 | C22 | semidirect |
| 9. C2×C22⋊Dic197 | C22 | semidirect |
| 10. C2×C22⋊Dic197 | C22 | semidirect |
| 11. #20263233 | C22 | semidirect |
| 15. C22×D4×C197 | C4 | semidirect |
| 28. C24×C197 | C2×C4 | semidirect |
| 36. C2×D4×C197 | C2×C4 | semidirect |
| 38. C22×C4×C197 | C2×C4 | semidirect |
| 52. C23×C197 | C22⋊C4 | semidirect |
| 87. C197 | #2308 | semidirect |
| 97. C22×D4 | Dic197 | semidirect |
| 110. C24 | C2×Dic197 | semidirect |
| 118. C2×D4 | C2×Dic197 | semidirect |
| 123. C22×C4 | C2×Dic197 | semidirect |
| 137. C23 | C22⋊Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic197 | 2 |
| #27160959 | 2 |
| #27160942 | 2 |
| #27160935 | 2 |
| C23×D4×C197 | 2 |
| #2308 | 197 |