Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15691346 | C2 | semidirect |
| 2. #27161650 | C2 | semidirect |
| 3. #27161554 | C2 | semidirect |
| 4. #27161292 | C2 | semidirect |
| 5. #27161282 | C2 | semidirect |
| 6. #27161107 | C2 | semidirect |
| 7. #27161089 | C2 | semidirect |
| 8. #27161075 | C2 | semidirect |
| 14. #20263324 | C22 | semidirect |
| 15. #20263313 | C22 | semidirect |
| 23. #20263255 | C22 | semidirect |
| 24. #20263251 | C22 | semidirect |
| 25. #20263250 | C22 | semidirect |
| 26. #20263247 | C22 | semidirect |
| 116. C197 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691346 | 2 |
| #27161650 | 2 |
| #27161554 | 2 |
| #27161292 | 2 |
| #27161282 | 2 |
| #27161107 | 2 |
| #27161089 | 2 |
| #27161075 | 2 |
| C2×AGL(1,ℤ/8)×C197 | 2 |
| #3042 | 197 |