Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 3. #27161380 | C2 | semidirect |
| 4. #27161380 | C2 | semidirect |
| 5. #27161370 | C2 | semidirect |
| 6. #27161360 | C2 | semidirect |
| 7. #27161121 | C2 | semidirect |
| 8. #27161117 | C2 | semidirect |
| 11. #424×C197 | C2 | semidirect |
| 13. #20263326 | C22 | semidirect |
| 15. #20263318 | 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. C4⋊C8×C197 | C22 | semidirect |
| 40. C4⋊C8×C197 | C22 | semidirect |
| 45. C2×D788 | Q8 | semidirect |
| 124. C197 | #3081 | semidirect |
| 134. #424 | D197 | semidirect |
| 160. C4⋊C8 | C2×D197 | semidirect |
| 161. C4⋊C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161707 | 2 |
| #27161553 | 2 |
| #27161380 | 2 |
| #27161370 | 2 |
| #27161360 | 2 |
| #27161121 | 2 |
| #27161117 | 2 |
| #27161085 | 2 |
| C2×#20263248 | 2 |
| #424×C197 | 2 |
| #3081 | 197 |