Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #27160976 | C2 | semidirect |
| 6. #27160949 | C2 | semidirect |
| 7. #27160948 | C2 | semidirect |
| 8. #27160944 | C2 | semidirect |
| 9. #382×C197 | C2 | semidirect |
| 13. #20263283 | C4 | semidirect |
| 45. #15691337 | C2×C4 | semidirect |
| 49. C4×Dic197 | C2×C4 | semidirect |
| 56. C42×C197 | C2×C4 | semidirect |
| 73. C4×D197 | C4⋊C4 | semidirect |
| 109. C197 | #2317 | semidirect |
| 119. #382 | D197 | semidirect |
| 166. C42 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263284 | 2 |
| C2×#20263283 | 2 |
| C2×C4⋊C4×D197 | 2 |
| #27160976 | 2 |
| #27160953 | 2 |
| #27160949 | 2 |
| #27160948 | 2 |
| #27160944 | 2 |
| #382×C197 | 2 |
| #2317 | 197 |