Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 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×#20263355 | C2 | semidirect |
| 3. C2×Q16×D197 | C2 | semidirect |
| 4. #27161649 | C2 | semidirect |
| 5. #27161474 | C2 | semidirect |
| 6. #27161470 | C2 | semidirect |
| 7. #27161462 | C2 | semidirect |
| 8. #27161459 | C2 | semidirect |
| 9. #27161457 | C2 | semidirect |
| 10. #27161033 | C2 | semidirect |
| 11. #495×C197 | C2 | semidirect |
| 121. C197 | #3156 | semidirect |
| 130. #495 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263355 | 2 |
| C2×#20263345 | 2 |
| C2×Q16×D197 | 2 |
| #27161649 | 2 |
| #27161474 | 2 |
| #27161470 | 2 |
| #27161462 | 2 |
| #27161459 | 2 |
| #27161457 | 2 |
| #27161033 | 2 |
| #495×C197 | 2 |
| #3156 | 197 |