Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#20263356 | C2 | semidirect |
| 3. C2×#20263314 | C2 | semidirect |
| 4. #27161301 | C2 | semidirect |
| 5. #27161294 | C2 | semidirect |
| 6. #27161103 | C2 | semidirect |
| 7. #27161087 | C2 | semidirect |
| 8. #27161083 | C2 | semidirect |
| 9. C4×#41×C197 | C2 | semidirect |
| 14. C2×#15691348 | C22 | semidirect |
| 15. C2×#15691346 | C22 | semidirect |
| 24. C4⋊#13096802 | C22 | semidirect |
| 25. #20263249 | C22 | semidirect |
| 28. C4×Q8×C197 | C22 | semidirect |
| 30. C4×D4×C197 | C22 | semidirect |
| 125. C197 | #3040 | semidirect |
| 130. C4×#41 | D197 | semidirect |
| 150. C4×Q8 | C2×D197 | semidirect |
| 152. C4×D4 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263356 | 2 |
| C2×#20263351 | 2 |
| C2×#20263314 | 2 |
| #27161301 | 2 |
| #27161294 | 2 |
| #27161103 | 2 |
| #27161087 | 2 |
| #27161083 | 2 |
| C4×#41×C197 | 2 |
| #3040 | 197 |