Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161707 | C2 | semidirect |
| 3. #27161446 | C2 | semidirect |
| 4. #27161440 | C2 | semidirect |
| 5. #27161435 | C2 | semidirect |
| 6. #27161428 | C2 | semidirect |
| 9. C2×#20263250 | C2 | semidirect |
| 10. #27161037 | C2 | semidirect |
| 11. #419×C197 | C2 | semidirect |
| 127. C197 | #3137 | semidirect |
| 135. #419 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161707 | 2 |
| #27161653 | 2 |
| #27161446 | 2 |
| #27161440 | 2 |
| #27161435 | 2 |
| #27161428 | 2 |
| #27161081 | 2 |
| #27161073 | 2 |
| C2×#20263250 | 2 |
| #27161037 | 2 |
| #419×C197 | 2 |
| #3137 | 197 |