Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161732 | C2 | semidirect |
| 2. D4×D788 | C2 | semidirect |
| 3. #27161427 | C2 | semidirect |
| 4. #27161394 | C2 | semidirect |
| 5. #27161316 | C2 | semidirect |
| 6. #27161275 | C2 | semidirect |
| 7. #27161214 | C2 | semidirect |
| 8. C4×#15691343 | C2 | semidirect |
| 9. #27161144 | C2 | semidirect |
| 10. #102×D197 | C2 | semidirect |
| 11. #474×C197 | C2 | semidirect |
| 15. C2×D1576 | C22 | semidirect |
| 17. C2×C8×D197 | C22 | semidirect |
| 22. #20263301 | C22 | semidirect |
| 26. C4×D788 | C22 | semidirect |
| 27. C4⋊C4×D197 | C22 | semidirect |
| 28. #20263259 | C22 | semidirect |
| 29. #20263248 | C22 | semidirect |
| 31. #20263246 | C22 | semidirect |
| 32. #20263246 | C22 | semidirect |
| 33. #20263246 | C22 | semidirect |
| 34. #20263238 | C22 | semidirect |
| 35. C4×#13096802 | C22 | semidirect |
| 36. C4⋊Q8×C197 | C22 | semidirect |
| 38. #107×C197 | C22 | semidirect |
| 39. C4⋊C8×C197 | C22 | semidirect |
| 92. D788 | D8 | semidirect |
| 105. D4×C197 | #41 | semidirect |
| 142. C197 | #3294 | semidirect |
| 148. #474 | D197 | semidirect |
| 161. C4⋊Q8 | C2×D197 | semidirect |
| 174. #107 | C2×D197 | semidirect |
| 175. C4⋊C8 | C2×D197 | semidirect |
| 240. D4 | #15691359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161732 | 2 |
| D4×D788 | 2 |
| #27161427 | 2 |
| #27161394 | 2 |
| #27161316 | 2 |
| #27161275 | 2 |
| #27161214 | 2 |
| C4×#15691343 | 2 |
| #27161144 | 2 |
| #102×D197 | 2 |
| #474×C197 | 2 |
| #3294 | 197 |