Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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. C2×#20263357 | C2 | semidirect |
| 2. C2×#20263351 | C2 | semidirect |
| 3. C2×#20263346 | C2 | semidirect |
| 4. C22×#15691345 | C2 | semidirect |
| 5. #27161648 | C2 | semidirect |
| 6. #27161471 | C2 | semidirect |
| 7. #27161469 | C2 | semidirect |
| 8. #27161461 | C2 | semidirect |
| 9. #27161453 | C2 | semidirect |
| 10. #27161035 | C2 | semidirect |
| 11. #536×C197 | C2 | semidirect |
| 17. C2×#15691348 | C22 | semidirect |
| 18. C2×#15691348 | C22 | semidirect |
| 19. C2×#15691346 | C22 | semidirect |
| 24. C2×#15691345 | C22 | semidirect |
| 25. C2×#15691345 | C22 | semidirect |
| 27. C2×#15691343 | C22 | semidirect |
| 34. #20263237 | C22 | semidirect |
| 35. C4×#13096802 | C22 | semidirect |
| 38. C4⋊Q8×C197 | C22 | semidirect |
| 39. #124×C197 | C22 | semidirect |
| 65. #15691342 | D4 | semidirect |
| 66. C2×#13096802 | D4 | semidirect |
| 148. C197 | #3154 | semidirect |
| 154. #536 | D197 | semidirect |
| 181. C4⋊Q8 | C2×D197 | semidirect |
| 184. #124 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263357 | 2 |
| C2×#20263351 | 2 |
| C2×#20263346 | 2 |
| C22×#15691345 | 2 |
| #27161648 | 2 |
| #27161471 | 2 |
| #27161469 | 2 |
| #27161461 | 2 |
| #27161453 | 2 |
| #27161035 | 2 |
| #536×C197 | 2 |
| #3154 | 197 |