Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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×#20263354 | C2 | semidirect |
| 2. C2×#20263352 | C2 | semidirect |
| 3. C2×#20263322 | C2 | semidirect |
| 4. #27161547 | C2 | semidirect |
| 5. #27161278 | C2 | semidirect |
| 6. #27161273 | C2 | semidirect |
| 7. #27161102 | C2 | semidirect |
| 8. #27161083 | C2 | semidirect |
| 9. #418×C197 | C2 | semidirect |
| 15. C2×#15691347 | C22 | semidirect |
| 16. C2×#15691346 | C22 | semidirect |
| 17. C2×D1576 | C22 | semidirect |
| 18. C2×#15691343 | C22 | semidirect |
| 23. #20263291 | C22 | semidirect |
| 24. #20263288 | C22 | semidirect |
| 29. #20263255 | C22 | semidirect |
| 30. #20263246 | C22 | semidirect |
| 34. #102×C197 | C22 | semidirect |
| 37. #15691358 | D4 | semidirect |
| 79. Dic394 | C2×D4 | semidirect |
| 84. D788 | C2×D4 | semidirect |
| 125. Dic197 | AGL(1,ℤ/8) | semidirect |
| 132. C197 | #3038 | semidirect |
| 142. #418 | D197 | semidirect |
| 167. #102 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263354 | 2 |
| C2×#20263352 | 2 |
| C2×#20263322 | 2 |
| #27161547 | 2 |
| #27161278 | 2 |
| #27161273 | 2 |
| #27161102 | 2 |
| #27161083 | 2 |
| #418×C197 | 2 |
| #3038 | 197 |