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 |
|---|---|---|
| 2. C22×#15691345 | C2 | semidirect |
| 3. #27161553 | C2 | semidirect |
| 4. #27161291 | C2 | semidirect |
| 5. #27161281 | C2 | semidirect |
| 6. #27161106 | C2 | semidirect |
| 7. #27161088 | C2 | semidirect |
| 8. #27161075 | C2 | semidirect |
| 9. #536×C197 | C2 | semidirect |
| 22. C4⋊#13096802 | C22 | semidirect |
| 23. #20263250 | C22 | semidirect |
| 24. #20263250 | C22 | semidirect |
| 25. #20263247 | C22 | semidirect |
| 28. C4⋊Q8×C197 | C22 | semidirect |
| 29. #124×C197 | C22 | semidirect |
| 116. C197 | #3042 | semidirect |
| 120. #536 | D197 | semidirect |
| 137. C4⋊Q8 | C2×D197 | semidirect |
| 138. #124 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| C22×#15691345 | 2 |
| #27161553 | 2 |
| #27161291 | 2 |
| #27161281 | 2 |
| #27161106 | 2 |
| #27161088 | 2 |
| #27161075 | 2 |
| #536×C197 | 2 |
| #3042 | 197 |