Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 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×#20263373 | C2 | semidirect |
| 2. C2×#20263354 | C2 | semidirect |
| 3. C2×#20263351 | C2 | semidirect |
| 4. C2×#20263314 | C2 | semidirect |
| 5. #27161253 | C2 | direct (N × H) |
| 6. C2×#20263254 | C2 | semidirect |
| 7. C2×#20263244 | C2 | semidirect |
| 8. C2×#104×C197 | C2 | semidirect |
| 12. #20263373 | C22 | semidirect |
| 22. #20263354 | C22 | semidirect |
| 24. #20263351 | C22 | semidirect |
| 31. #20263314 | C22 | semidirect |
| 33. #20263254 | C22 | semidirect |
| 34. #20263244 | C22 | semidirect |
| 38. #104×C197 | C22 | semidirect |
| 171. C2×C197 | #454 | semidirect |
| 175. C197 | C2×#454 | semidirect |
| 183. C2×#104 | D197 | semidirect |
| 213. #104 | C2×D197 | semidirect |
| 349. C2 | #27161253 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263373 | 2 |
| C2×#20263354 | 2 |
| C2×#20263351 | 2 |
| C2×#20263314 | 2 |
| #27161253 | 2 |
| C2×#20263254 | 2 |
| C2×#20263244 | 2 |
| C2×#104×C197 | 2 |
| C2×#454 | 197 |