Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#20263345 | C2 | semidirect |
| 2. #27161728 | C2 | semidirect |
| 3. #27161457 | C2 | semidirect |
| 4. #27161320 | C2 | semidirect |
| 5. #27161317 | C2 | semidirect |
| 6. #27161282 | C2 | semidirect |
| 7. #27161241 | C2 | semidirect |
| 8. #27161238 | C2 | semidirect |
| 9. D8×Dic197 | C2 | semidirect |
| 10. C8×C22⋊D197 | C2 | semidirect |
| 11. C2×#135×C197 | C2 | semidirect |
| 76. D8×C197 | D4 | semidirect |
| 129. Dic197 | #135 | semidirect |
| 136. C197 | #3283 | semidirect |
| 139. C2×#135 | D197 | semidirect |
| 198. D8 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263345 | 2 |
| #27161728 | 2 |
| #27161457 | 2 |
| #27161320 | 2 |
| #27161317 | 2 |
| #27161282 | 2 |
| #27161241 | 2 |
| #27161238 | 2 |
| D8×Dic197 | 2 |
| C8×C22⋊D197 | 2 |
| C2×#135×C197 | 2 |
| #3283 | 197 |