Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #27161562 | C2 | semidirect |
| 3. #27161404 | C2 | semidirect |
| 4. #27161404 | C2 | semidirect |
| 5. #27161398 | C2 | semidirect |
| 6. #27161393 | C2 | semidirect |
| 7. #27161121 | C2 | semidirect |
| 8. #27161117 | C2 | semidirect |
| 9. #27161085 | C2 | semidirect |
| 10. C2×#20263248 | C2 | semidirect |
| 11. #408×C197 | C2 | semidirect |
| 23. #20263285 | C22 | semidirect |
| 25. C2×C4⋊Dic197 | C22 | semidirect |
| 26. #20263260 | C22 | semidirect |
| 27. #20263260 | C22 | semidirect |
| 28. #20263260 | C22 | semidirect |
| 29. #20263258 | C22 | semidirect |
| 30. #20263258 | C22 | semidirect |
| 31. #20263258 | C22 | semidirect |
| 39. C22⋊C8×C197 | C22 | semidirect |
| 40. C22⋊C8×C197 | C22 | semidirect |
| 134. C197 | #3096 | semidirect |
| 146. #408 | D197 | semidirect |
| 174. C22⋊C8 | C2×D197 | semidirect |
| 175. C22⋊C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161643 | 2 |
| #27161562 | 2 |
| #27161404 | 2 |
| #27161398 | 2 |
| #27161393 | 2 |
| #27161121 | 2 |
| #27161117 | 2 |
| #27161085 | 2 |
| C2×#20263248 | 2 |
| #408×C197 | 2 |
| #3096 | 197 |