Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 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. #27161707 | C2 | semidirect |
| 2. #27161379 | C2 | semidirect |
| 3. #27161379 | C2 | semidirect |
| 4. #27161369 | C2 | semidirect |
| 5. #27161359 | C2 | semidirect |
| 6. #27161122 | C2 | semidirect |
| 7. #27161115 | C2 | semidirect |
| 8. #27161106 | C2 | semidirect |
| 14. #20263326 | C22 | semidirect |
| 16. #20263318 | C22 | semidirect |
| 21. #20263259 | C22 | semidirect |
| 22. #20263259 | C22 | semidirect |
| 23. #20263259 | C22 | semidirect |
| 24. #20263257 | C22 | semidirect |
| 25. #20263257 | C22 | semidirect |
| 26. #20263257 | C22 | semidirect |
| 27. C4⋊#13096802 | C22 | semidirect |
| 28. C4⋊#13096802 | C22 | semidirect |
| 60. C2×D4×C197 | Q8 | semidirect |
| 124. C197 | #3081 | semidirect |
| 170. C2×D4 | Dic394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161707 | 2 |
| #27161379 | 2 |
| #27161369 | 2 |
| #27161359 | 2 |
| #27161122 | 2 |
| #27161115 | 2 |
| #27161106 | 2 |
| #27161084 | 2 |
| C2×#20263247 | 2 |
| #518×C197 | 2 |
| #3081 | 197 |