Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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×#20263351 | C2 | semidirect |
| 2. C22×D1576 | C2 | semidirect |
| 3. #27161643 | C2 | semidirect |
| 4. #27161465 | C2 | semidirect |
| 5. #27161464 | C2 | semidirect |
| 6. #27161454 | C2 | semidirect |
| 7. #27161034 | C2 | semidirect |
| 8. C2×#135×C197 | C2 | semidirect |
| 11. C2×#15691345 | C22 | semidirect |
| 15. C2×#15691343 | C22 | semidirect |
| 17. #20263322 | C22 | semidirect |
| 18. #20263315 | C22 | semidirect |
| 22. #20263236 | C22 | semidirect |
| 23. C8×Dic197 | C22 | semidirect |
| 26. C2×Q16×C197 | C22 | semidirect |
| 27. C2×SD16×C197 | C22 | semidirect |
| 28. C2×D8×C197 | C22 | semidirect |
| 40. #15691342 | D4 | semidirect |
| 56. C2×C8×C197 | D4 | semidirect |
| 101. C197 | #3155 | semidirect |
| 104. C2×#135 | D197 | semidirect |
| 115. C2×Q16 | C2×D197 | semidirect |
| 117. C2×SD16 | C2×D197 | semidirect |
| 122. C2×D8 | C2×D197 | semidirect |
| 154. 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×#20263351 | 2 |
| C22×D1576 | 2 |
| #27161643 | 2 |
| #27161465 | 2 |
| #27161464 | 2 |
| #27161454 | 2 |
| #27161034 | 2 |
| C2×#135×C197 | 2 |
| #3155 | 197 |