Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 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 |
|---|---|---|
| 1. C22×#15691358 | C2 | semidirect |
| 2. C2×#20263354 | C2 | semidirect |
| 3. C2×#20263300 | C2 | semidirect |
| 4. #27161226 | C2 | semidirect |
| 5. #27161220 | C2 | semidirect |
| 6. #27161215 | C2 | semidirect |
| 7. #27161081 | C2 | semidirect |
| 8. #407×C197 | C2 | semidirect |
| 13. C2×#15691358 | C22 | semidirect |
| 14. C22×Dic394 | C22 | semidirect |
| 15. C22×D788 | C22 | semidirect |
| 16. C22×D788 | C22 | semidirect |
| 21. C2×#15691347 | C22 | semidirect |
| 22. C2×D1576 | C22 | semidirect |
| 26. #20263300 | C22 | semidirect |
| 27. C2×C4⋊Dic197 | C22 | semidirect |
| 29. #20263251 | C22 | semidirect |
| 30. #20263248 | C22 | semidirect |
| 32. C2×M16×C197 | C22 | semidirect |
| 33. C22⋊C8×C197 | C22 | semidirect |
| 34. C22⋊C8×C197 | C22 | semidirect |
| 42. #15691358 | D4 | semidirect |
| 89. Dic394 | C2×D4 | semidirect |
| 94. D788 | C2×D4 | semidirect |
| 131. C22×C197 | AGL(1,ℤ/8) | semidirect |
| 155. C197 | #3006 | semidirect |
| 164. #407 | D197 | semidirect |
| 180. C2×M16 | C2×D197 | semidirect |
| 189. C22⋊C8 | C2×D197 | semidirect |
| 190. C22⋊C8 | C2×D197 | semidirect |
| 295. C22 | #20263354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691358 | 2 |
| C2×#20263354 | 2 |
| C2×#20263300 | 2 |
| #27161226 | 2 |
| #27161220 | 2 |
| #27161215 | 2 |
| #27161081 | 2 |
| #407×C197 | 2 |
| #3006 | 197 |