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×#20263348 | C2 | semidirect |
| 2. #27161590 | C2 | semidirect |
| 3. #27161337 | C2 | semidirect |
| 4. #27161332 | C2 | semidirect |
| 5. #27161325 | C2 | semidirect |
| 6. #27161117 | C2 | semidirect |
| 7. #27161076 | C2 | semidirect |
| 8. C22×M16×C197 | C2 | semidirect |
| 11. C2×Dic788 | C22 | semidirect |
| 12. C2×#15691347 | C22 | semidirect |
| 13. C2×D1576 | C22 | semidirect |
| 20. #20263260 | C22 | semidirect |
| 21. #20263258 | C22 | semidirect |
| 22. #20263251 | C22 | semidirect |
| 23. #20263248 | C22 | semidirect |
| 56. C2×C8×C197 | D4 | semidirect |
| 105. C197 | #3054 | semidirect |
| 108. C22×M16 | D197 | semidirect |
| 156. C2×C8 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263348 | 2 |
| #27161590 | 2 |
| #27161337 | 2 |
| #27161332 | 2 |
| #27161325 | 2 |
| #27161117 | 2 |
| #27161076 | 2 |
| C22×M16×C197 | 2 |
| #3054 | 197 |