Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#15691357 | C2 | semidirect |
| 2. C2×#20263356 | C2 | semidirect |
| 3. #27161586 | C2 | semidirect |
| 4. #27161238 | C2 | semidirect |
| 5. #27161221 | C2 | semidirect |
| 6. #27161089 | C2 | semidirect |
| 7. #27161084 | C2 | semidirect |
| 8. #27161042 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C197 | C2 | semidirect |
| 19. C2×#15691348 | C22 | semidirect |
| 20. C2×#15691346 | C22 | semidirect |
| 23. #20263302 | C22 | semidirect |
| 24. #20263297 | C22 | semidirect |
| 28. #20263251 | C22 | semidirect |
| 29. #20263247 | C22 | semidirect |
| 30. #20263238 | C22 | semidirect |
| 34. C2×SD16×C197 | C22 | semidirect |
| 35. C2×D8×C197 | C22 | semidirect |
| 43. C2×Dic394 | D4 | semidirect |
| 73. C2×D4×C197 | D4 | semidirect |
| 145. C197 | #3005 | semidirect |
| 149. C2×AGL(1,ℤ/8) | D197 | semidirect |
| 170. C2×SD16 | C2×D197 | semidirect |
| 171. C2×D8 | C2×D197 | semidirect |
| 201. C2×D4 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691357 | 2 |
| C2×#20263356 | 2 |
| #27161586 | 2 |
| #27161238 | 2 |
| #27161221 | 2 |
| #27161089 | 2 |
| #27161084 | 2 |
| #27161042 | 2 |
| C2×AGL(1,ℤ/8)×C197 | 2 |
| #3005 | 197 |