Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#15691359 | C2 | semidirect |
| 2. C22×#15691345 | C2 | semidirect |
| 3. C22×D1576 | C2 | semidirect |
| 4. C2×#20263301 | C2 | semidirect |
| 5. #27161227 | C2 | direct (N × H) |
| 6. C2×#20263246 | C2 | semidirect |
| 7. C2×#20263238 | C2 | semidirect |
| 8. C2×#103×C197 | C2 | semidirect |
| 12. C2×#15691359 | C22 | semidirect |
| 20. C2×#15691345 | C22 | semidirect |
| 22. C2×D1576 | C22 | semidirect |
| 25. #20263301 | C22 | semidirect |
| 27. #20263246 | C22 | semidirect |
| 28. #20263238 | C22 | semidirect |
| 32. #103×C197 | C22 | semidirect |
| 48. C2×D788 | D4 | semidirect |
| 65. C2×Q8×C197 | D4 | semidirect |
| 93. D788 | C2×D4 | semidirect |
| 104. Q8×C197 | C2×D4 | semidirect |
| 136. C2×C197 | #449 | semidirect |
| 143. C197 | C2×#449 | semidirect |
| 150. C2×#103 | D197 | semidirect |
| 174. #103 | C2×D197 | semidirect |
| 185. C2×Q8 | D788 | semidirect |
| 233. Q8 | C2×D788 | semidirect |
| 283. C2 | #27161227 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691359 | 2 |
| C22×#15691345 | 2 |
| C22×D1576 | 2 |
| C2×#20263301 | 2 |
| #27161227 | 2 |
| C2×#20263246 | 2 |
| C2×#20263238 | 2 |
| C2×#103×C197 | 2 |
| C2×#449 | 197 |