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. #27161178 | C2 | semidirect |
| 5. #27161166 | C2 | semidirect |
| 6. #27161087 | C2 | semidirect |
| 8. #27161034 | C2 | semidirect |
| 9. #427×C197 | C2 | semidirect |
| 12. C2×#15691347 | C4 | semidirect |
| 17. #20263291 | C22 | semidirect |
| 23. #20263249 | C22 | semidirect |
| 25. #20263236 | C22 | semidirect |
| 26. C8×Dic197 | C22 | semidirect |
| 30. #107×C197 | C22 | semidirect |
| 31. #106×C197 | C22 | semidirect |
| 35. C2×Dic394 | C2×C4 | semidirect |
| 43. #15691347 | C2×C4 | semidirect |
| 44. #15691347 | C2×C4 | semidirect |
| 54. C2×C8×C197 | C2×C4 | semidirect |
| 103. C197 | #2949 | semidirect |
| 110. #427 | D197 | semidirect |
| 130. #107 | C2×D197 | semidirect |
| 131. #106 | C2×D197 | semidirect |
| 152. C2×C8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691347 | 2 |
| #27161556 | 2 |
| #27161553 | 2 |
| #27161178 | 2 |
| #27161166 | 2 |
| #27161087 | 2 |
| #27161083 | 2 |
| #27161034 | 2 |
| #427×C197 | 2 |
| #2949 | 197 |