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×#20263374 | C2 | semidirect |
| 2. C2×#20263346 | C2 | semidirect |
| 3. #27161657 | C2 | semidirect |
| 4. #27161240 | C2 | semidirect |
| 5. #27161233 | C2 | semidirect |
| 6. #27161223 | C2 | semidirect |
| 7. #27161216 | C2 | semidirect |
| 8. #27161081 | C2 | semidirect |
| 9. C2×#20263250 | C2 | semidirect |
| 10. #27161047 | C2 | semidirect |
| 11. C2×#137×C197 | C2 | semidirect |
| 52. #15691358 | D4 | semidirect |
| 86. C2×Q8×C197 | D4 | semidirect |
| 169. C197 | #3013 | semidirect |
| 172. C2×#137 | D197 | semidirect |
| 233. C2×Q8 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263374 | 2 |
| C2×#20263346 | 2 |
| #27161657 | 2 |
| #27161240 | 2 |
| #27161233 | 2 |
| #27161223 | 2 |
| #27161216 | 2 |
| #27161081 | 2 |
| C2×#20263250 | 2 |
| #27161047 | 2 |
| C2×#137×C197 | 2 |
| #3013 | 197 |