Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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×#20263348 | C2 | semidirect |
| 2. C2×Q16×D197 | C2 | semidirect |
| 3. #27161739 | C2 | semidirect |
| 4. #27161464 | C2 | semidirect |
| 5. #27161316 | C2 | semidirect |
| 6. #27161304 | C2 | semidirect |
| 7. #27161239 | C2 | semidirect |
| 8. #27161219 | C2 | semidirect |
| 9. #27161173 | C2 | semidirect |
| 10. C8×C22⋊D197 | C2 | semidirect |
| 11. #467×C197 | C2 | semidirect |
| 54. Dic788 | D4 | semidirect |
| 120. C2×D197 | #135 | semidirect |
| 136. C197 | #3285 | semidirect |
| 142. #467 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263348 | 2 |
| C2×Q16×D197 | 2 |
| #27161739 | 2 |
| #27161464 | 2 |
| #27161316 | 2 |
| #27161304 | 2 |
| #27161239 | 2 |
| #27161219 | 2 |
| #27161173 | 2 |
| C8×C22⋊D197 | 2 |
| #467×C197 | 2 |
| #3285 | 197 |