Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27161624 | C2 | semidirect |
| 2. #27161483 | C2 | semidirect |
| 3. #27161454 | C2 | semidirect |
| 4. #27161424 | C2 | semidirect |
| 5. #27161315 | C2 | semidirect |
| 6. #27161313 | C2 | semidirect |
| 7. D8×Dic197 | C2 | semidirect |
| 8. #27161161 | C2 | semidirect |
| 9. #27161159 | C2 | semidirect |
| 10. C2×C8×Dic197 | C2 | semidirect |
| 11. #466×C197 | C2 | semidirect |
| 82. C2×Dic197 | D8 | semidirect |
| 89. #13096802 | #41 | semidirect |
| 101. C8×C197 | #41 | semidirect |
| 127. C197 | #3169 | semidirect |
| 135. #466 | D197 | semidirect |
| 229. C8 | #15691357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161624 | 2 |
| #27161483 | 2 |
| #27161454 | 2 |
| #27161424 | 2 |
| #27161315 | 2 |
| #27161313 | 2 |
| D8×Dic197 | 2 |
| #27161161 | 2 |
| #27161159 | 2 |
| C2×C8×Dic197 | 2 |
| #466×C197 | 2 |
| #3169 | 197 |