Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 484 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. #27161560 | C2 | semidirect |
| 3. #27161190 | C2 | semidirect |
| 4. #27161185 | C2 | semidirect |
| 5. #27161166 | C2 | semidirect |
| 6. #27161078 | C2 | semidirect |
| 7. #27161034 | C2 | semidirect |
| 8. C2×#106×C197 | C2 | semidirect |
| 10. #20263348 | C4 | semidirect |
| 30. #15691358 | C2×C4 | semidirect |
| 36. Dic788 | C2×C4 | semidirect |
| 37. #15691347 | C2×C4 | semidirect |
| 38. D1576 | C2×C4 | semidirect |
| 49. C2×C8×C197 | C2×C4 | semidirect |
| 90. C197 | #2952 | semidirect |
| 97. C2×#106 | D197 | semidirect |
| 134. C2×C8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263348 | 2 |
| #27161560 | 2 |
| #27161190 | 2 |
| #27161185 | 2 |
| #27161166 | 2 |
| #27161078 | 2 |
| #27161034 | 2 |
| C2×#106×C197 | 2 |
| #2952 | 197 |