Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27161691 | C2 | semidirect |
| 3. #27161421 | C2 | semidirect |
| 4. #27161380 | C2 | semidirect |
| 5. #27161285 | C2 | semidirect |
| 7. #27161181 | C2 | semidirect |
| 8. C4×#15691347 | C2 | semidirect |
| 9. #433×C197 | C2 | semidirect |
| 13. #20263326 | C22 | semidirect |
| 15. #20263318 | C22 | semidirect |
| 18. C4×Dic394 | C22 | semidirect |
| 24. #20263260 | C22 | semidirect |
| 25. #20263258 | C22 | semidirect |
| 26. #20263251 | C22 | semidirect |
| 27. #20263251 | C22 | semidirect |
| 31. C4⋊C8×C197 | C22 | semidirect |
| 33. #97×C197 | C22 | semidirect |
| 34. C4×C8×C197 | C22 | semidirect |
| 102. C197 | #3123 | semidirect |
| 112. #433 | D197 | semidirect |
| 130. C4⋊C8 | C2×D197 | semidirect |
| 136. #97 | C2×D197 | semidirect |
| 137. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161691 | 2 |
| #27161553 | 2 |
| #27161421 | 2 |
| #27161380 | 2 |
| #27161285 | 2 |
| #27161232 | 2 |
| #27161181 | 2 |
| C4×#15691347 | 2 |
| #433×C197 | 2 |
| #3123 | 197 |