Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20263373 | C2 | semidirect |
| 2. C2×#20263359 | C2 | semidirect |
| 3. C2×#20263346 | C2 | semidirect |
| 4. #27161660 | C2 | semidirect |
| 5. #27161242 | C2 | semidirect |
| 6. #27161236 | C2 | semidirect |
| 7. #27161225 | C2 | semidirect |
| 8. #27161219 | C2 | semidirect |
| 9. C2×#20263249 | C2 | semidirect |
| 10. #27161047 | C2 | semidirect |
| 11. #417×C197 | C2 | semidirect |
| 58. C2×Dic394 | D4 | semidirect |
| 87. #41×C197 | D4 | semidirect |
| 169. C197 | #3013 | semidirect |
| 179. #417 | D197 | semidirect |
| 224. #41 | D788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263373 | 2 |
| C2×#20263359 | 2 |
| C2×#20263346 | 2 |
| #27161660 | 2 |
| #27161242 | 2 |
| #27161236 | 2 |
| #27161225 | 2 |
| #27161219 | 2 |
| C2×#20263249 | 2 |
| #27161047 | 2 |
| #417×C197 | 2 |
| #3013 | 197 |