Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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×#20263359 | C2 | semidirect |
| 3. C2×#20263305 | C2 | semidirect |
| 4. #27161243 | C2 | semidirect |
| 5. #27161237 | C2 | semidirect |
| 6. #27161232 | C2 | semidirect |
| 7. #27161081 | C2 | semidirect |
| 8. #407×C197 | C2 | semidirect |
| 15. C22×Dic394 | C22 | semidirect |
| 20. C2×Dic788 | C22 | semidirect |
| 21. C2×#15691347 | C22 | semidirect |
| 25. #20263305 | C22 | semidirect |
| 26. C2×C4⋊Dic197 | C22 | semidirect |
| 29. #20263251 | C22 | semidirect |
| 30. #20263248 | C22 | semidirect |
| 32. C2×M16×C197 | C22 | semidirect |
| 34. C22⋊C8×C197 | C22 | semidirect |
| 126. C22×C197 | #137 | semidirect |
| 146. C197 | #3007 | semidirect |
| 155. #407 | D197 | semidirect |
| 170. C2×M16 | C2×D197 | semidirect |
| 181. C22⋊C8 | C2×D197 | semidirect |
| 277. C22 | #20263359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691358 | 2 |
| C2×#20263359 | 2 |
| C2×#20263305 | 2 |
| #27161243 | 2 |
| #27161237 | 2 |
| #27161232 | 2 |
| #27161081 | 2 |
| #407×C197 | 2 |
| #3007 | 197 |