Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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. C22×#15691346 | C2 | semidirect |
| 3. #27161646 | C2 | semidirect |
| 4. #27161221 | C2 | semidirect |
| 5. #27161216 | C2 | semidirect |
| 6. #27161089 | C2 | semidirect |
| 7. #27161075 | C2 | semidirect |
| 8. #27161047 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C197 | C2 | semidirect |
| 15. C2×#15691357 | C22 | semidirect |
| 18. C2×Q8×D197 | C22 | semidirect |
| 27. #20263251 | C22 | semidirect |
| 28. #20263250 | C22 | semidirect |
| 29. #20263247 | C22 | semidirect |
| 30. #20263238 | C22 | semidirect |
| 48. C2×Dic394 | D4 | semidirect |
| 69. #41×C197 | D4 | semidirect |
| 145. C197 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D197 | semidirect |
| 191. #41 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263373 | 2 |
| C22×#15691346 | 2 |
| #27161646 | 2 |
| #27161221 | 2 |
| #27161216 | 2 |
| #27161089 | 2 |
| #27161075 | 2 |
| #27161047 | 2 |
| C2×AGL(1,ℤ/8)×C197 | 2 |
| #3010 | 197 |