Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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×#20263347 | C2 | semidirect |
| 2. C2×#20263345 | C2 | semidirect |
| 3. #27161628 | C2 | semidirect |
| 4. #27161627 | C2 | semidirect |
| 5. #27161474 | C2 | semidirect |
| 6. #27161473 | C2 | semidirect |
| 7. #27161470 | C2 | semidirect |
| 8. #27161467 | C2 | semidirect |
| 9. #27161466 | C2 | semidirect |
| 10. #97×D197 | C2 | semidirect |
| 11. #496×C197 | C2 | semidirect |
| 64. C8×D197 | D4 | semidirect |
| 133. C197 | #3150 | semidirect |
| 144. #496 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263347 | 2 |
| C2×#20263345 | 2 |
| #27161628 | 2 |
| #27161627 | 2 |
| #27161474 | 2 |
| #27161473 | 2 |
| #27161470 | 2 |
| #27161467 | 2 |
| #27161466 | 2 |
| #97×D197 | 2 |
| #496×C197 | 2 |
| #3150 | 197 |