Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 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. #27161556 | C2 | semidirect |
| 4. #27161176 | C2 | semidirect |
| 5. #27161170 | C2 | semidirect |
| 6. #27161115 | C2 | semidirect |
| 7. #27161089 | C2 | semidirect |
| 8. #27161037 | C2 | semidirect |
| 11. C2×#15691346 | C4 | semidirect |
| 16. #20263291 | C22 | semidirect |
| 23. #20263259 | C22 | semidirect |
| 24. #20263257 | C22 | semidirect |
| 25. #20263251 | C22 | semidirect |
| 26. #20263236 | C22 | semidirect |
| 27. C8×Dic197 | C22 | semidirect |
| 34. C2×Dic394 | C2×C4 | semidirect |
| 38. #15691346 | C2×C4 | semidirect |
| 39. #15691346 | C2×C4 | semidirect |
| 40. C2×#13096802 | C2×C4 | semidirect |
| 103. C197 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691346 | 2 |
| #27161556 | 2 |
| #27161554 | 2 |
| #27161176 | 2 |
| #27161170 | 2 |
| #27161115 | 2 |
| #27161089 | 2 |
| #27161037 | 2 |
| #418×C197 | 2 |
| #2949 | 197 |