Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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×Q8×D197 | C2 | semidirect |
| 2. C2×#20263359 | C2 | semidirect |
| 3. C2×#20263357 | C2 | semidirect |
| 5. #27161236 | C2 | semidirect |
| 6. #27161219 | C2 | semidirect |
| 7. #27161087 | C2 | semidirect |
| 8. #27161042 | C2 | semidirect |
| 9. #419×C197 | C2 | semidirect |
| 21. C2×Dic788 | C22 | semidirect |
| 22. C2×#15691348 | C22 | semidirect |
| 23. C2×#15691347 | C22 | semidirect |
| 24. C2×#15691345 | C22 | semidirect |
| 31. #20263249 | C22 | semidirect |
| 36. #103×C197 | C22 | semidirect |
| 44. C2×Dic394 | D4 | semidirect |
| 73. C2×Q8×C197 | D4 | semidirect |
| 127. C2×D197 | #137 | semidirect |
| 141. C197 | #3004 | semidirect |
| 150. #419 | D197 | semidirect |
| 177. #103 | C2×D197 | semidirect |
| 194. C2×Q8 | D788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D197 | 2 |
| C2×#20263359 | 2 |
| C2×#20263357 | 2 |
| #27161591 | 2 |
| #27161236 | 2 |
| #27161219 | 2 |
| #27161087 | 2 |
| #27161042 | 2 |
| #419×C197 | 2 |
| #3004 | 197 |