Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#20263359 | C2 | semidirect |
| 2. C2×#20263346 | C2 | semidirect |
| 3. C22×#15691346 | C2 | semidirect |
| 4. #27161650 | C2 | semidirect |
| 5. #27161646 | C2 | semidirect |
| 6. #27161470 | C2 | semidirect |
| 7. #27161467 | C2 | semidirect |
| 8. #27161462 | C2 | semidirect |
| 9. #27161450 | C2 | semidirect |
| 10. #27161037 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C197 | C2 | semidirect |
| 16. C2×Dic788 | C22 | semidirect |
| 17. C2×#15691348 | C22 | semidirect |
| 18. C2×#15691347 | C22 | semidirect |
| 22. C2×#15691346 | C22 | semidirect |
| 23. C2×#15691345 | C22 | semidirect |
| 24. C2×#15691343 | C22 | semidirect |
| 26. #20263324 | C22 | semidirect |
| 29. #20263313 | C22 | semidirect |
| 35. #20263236 | C22 | semidirect |
| 36. C8×Dic197 | C22 | semidirect |
| 63. C2×#13096802 | D4 | semidirect |
| 86. M16×C197 | D4 | semidirect |
| 148. C197 | #3154 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D197 | semidirect |
| 226. M16 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263359 | 2 |
| C2×#20263346 | 2 |
| C22×#15691346 | 2 |
| #27161650 | 2 |
| #27161646 | 2 |
| #27161470 | 2 |
| #27161467 | 2 |
| #27161462 | 2 |
| #27161450 | 2 |
| #27161037 | 2 |
| C2×AGL(1,ℤ/8)×C197 | 2 |
| #3154 | 197 |