Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C2×Q8×Dic197 | C2 | semidirect |
| 3. #27161412 | C2 | semidirect |
| 5. #27161384 | C2 | semidirect |
| 6. #27161303 | C2 | semidirect |
| 8. #27161186 | C2 | semidirect |
| 9. #27161182 | C2 | semidirect |
| 10. #27161133 | C2 | semidirect |
| 11. #451×C197 | C2 | semidirect |
| 131. C197 | #3117 | semidirect |
| 139. #451 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161615 | 2 |
| C2×Q8×Dic197 | 2 |
| #27161412 | 2 |
| #27161398 | 2 |
| #27161384 | 2 |
| #27161303 | 2 |
| #27161218 | 2 |
| #27161186 | 2 |
| #27161182 | 2 |
| #27161133 | 2 |
| #451×C197 | 2 |
| #3117 | 197 |