Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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×#20263348 | C2 | semidirect |
| 2. C22×C8×D197 | C2 | semidirect |
| 3. #27161591 | C2 | semidirect |
| 4. #27161321 | C2 | semidirect |
| 5. #27161316 | C2 | semidirect |
| 6. #27161309 | C2 | semidirect |
| 7. #27161073 | C2 | semidirect |
| 8. #427×C197 | C2 | semidirect |
| 12. C2×Dic788 | C22 | semidirect |
| 13. C2×#15691347 | C22 | semidirect |
| 14. C2×D1576 | C22 | semidirect |
| 24. #20263249 | C22 | semidirect |
| 25. #20263246 | C22 | semidirect |
| 28. #107×C197 | C22 | semidirect |
| 29. #106×C197 | C22 | semidirect |
| 54. C2×C8×C197 | D4 | semidirect |
| 94. C2×D197 | #135 | semidirect |
| 106. C197 | #3050 | semidirect |
| 114. #427 | D197 | semidirect |
| 133. #107 | C2×D197 | semidirect |
| 134. #106 | C2×D197 | semidirect |
| 158. C2×C8 | D788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263348 | 2 |
| C22×C8×D197 | 2 |
| #27161591 | 2 |
| #27161321 | 2 |
| #27161316 | 2 |
| #27161309 | 2 |
| #27161073 | 2 |
| #427×C197 | 2 |
| #3050 | 197 |