Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161887 | C2 | semidirect |
| 2. #27161881 | C2 | semidirect |
| 3. #27161464 | C2 | semidirect |
| 4. #27161351 | C2 | semidirect |
| 5. #27161349 | C2 | semidirect |
| 6. #27161344 | C2 | semidirect |
| 7. #27161255 | C2 | semidirect |
| 8. #27161252 | C2 | semidirect |
| 9. #27161196 | C2 | semidirect |
| 10. #27161194 | C2 | semidirect |
| 11. #578×C197 | C2 | semidirect |
| 18. #20263351 | C22 | semidirect |
| 23. C2×#15691345 | C22 | semidirect |
| 26. #20263333 | C22 | semidirect |
| 28. #20263315 | C22 | semidirect |
| 29. #20263262 | C22 | semidirect |
| 30. #20263261 | C22 | semidirect |
| 31. #20263253 | C22 | semidirect |
| 32. #20263253 | C22 | semidirect |
| 34. #20263245 | C22 | semidirect |
| 35. #20263242 | C22 | semidirect |
| 36. C8×Dic197 | C22 | semidirect |
| 37. 2−1+4×C197 | C22 | semidirect |
| 39. #137×C197 | C22 | semidirect |
| 43. C2×Q16×C197 | C22 | semidirect |
| 44. #131×C197 | C22 | semidirect |
| 149. C197 | #3290 | semidirect |
| 151. #578 | D197 | semidirect |
| 162. 2−1+4 | C2×D197 | semidirect |
| 167. #137 | C2×D197 | semidirect |
| 178. C2×Q16 | C2×D197 | semidirect |
| 185. #131 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161887 | 2 |
| #27161881 | 2 |
| #27161464 | 2 |
| #27161351 | 2 |
| #27161349 | 2 |
| #27161344 | 2 |
| #27161255 | 2 |
| #27161252 | 2 |
| #27161196 | 2 |
| #27161194 | 2 |
| #578×C197 | 2 |
| #3290 | 197 |