Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #27161554 | C2 | semidirect |
| 3. #27161553 | C2 | semidirect |
| 4. #27161188 | C2 | semidirect |
| 5. #27161159 | C2 | semidirect |
| 6. #27161115 | C2 | semidirect |
| 7. #27161085 | C2 | semidirect |
| 8. #27161037 | C2 | semidirect |
| 9. #418×C197 | C2 | semidirect |
| 11. C2×#15691343 | C4 | semidirect |
| 17. D4×Dic197 | C22 | semidirect |
| 18. #20263288 | C22 | semidirect |
| 23. #20263259 | C22 | semidirect |
| 24. #20263257 | C22 | semidirect |
| 25. #20263248 | C22 | semidirect |
| 26. #20263236 | C22 | semidirect |
| 27. C8×Dic197 | C22 | semidirect |
| 31. #102×C197 | C22 | semidirect |
| 35. C2×D788 | C2×C4 | semidirect |
| 39. #15691343 | C2×C4 | semidirect |
| 40. #15691343 | C2×C4 | semidirect |
| 41. C2×#13096802 | C2×C4 | semidirect |
| 55. C2×D4×C197 | C2×C4 | semidirect |
| 108. C197 | #2948 | semidirect |
| 117. #418 | D197 | semidirect |
| 138. #102 | C2×D197 | semidirect |
| 149. C2×D4 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691343 | 2 |
| #27161554 | 2 |
| #27161553 | 2 |
| #27161188 | 2 |
| #27161159 | 2 |
| #27161115 | 2 |
| #27161085 | 2 |
| #27161037 | 2 |
| #418×C197 | 2 |
| #2948 | 197 |