Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #27161636 | C2 | semidirect |
| 3. #27161380 | C2 | semidirect |
| 4. #27161370 | C2 | semidirect |
| 5. #27161360 | C2 | semidirect |
| 6. #27161121 | C2 | semidirect |
| 8. #423×C197 | C2 | semidirect |
| 11. #20263326 | C22 | semidirect |
| 12. #20263326 | C22 | semidirect |
| 13. #20263318 | C22 | semidirect |
| 25. #20263260 | C22 | semidirect |
| 26. #20263258 | C22 | semidirect |
| 31. C4⋊C8×C197 | C22 | semidirect |
| 32. C4⋊C8×C197 | C22 | semidirect |
| 38. C2×D788 | Q8 | semidirect |
| 115. C197 | #3077 | semidirect |
| 123. #423 | D197 | semidirect |
| 145. C4⋊C8 | C2×D197 | semidirect |
| 146. C4⋊C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161636 | 2 |
| C2×C4×D788 | 2 |
| #27161380 | 2 |
| #27161370 | 2 |
| #27161360 | 2 |
| #27161121 | 2 |
| #27161085 | 2 |
| #423×C197 | 2 |
| #3077 | 197 |