Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #27161088 | C2 | semidirect |
| 5. #27160836 | C2 | semidirect |
| 6. #27160835 | C2 | semidirect |
| 7. #419×C197 | C2 | semidirect |
| 13. #20263324 | C4 | semidirect |
| 14. #20263315 | C4 | semidirect |
| 109. C197 | #1909 | semidirect |
| 114. #419 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161845 | 2 |
| #27161653 | 2 |
| #27161088 | 2 |
| #27161052 | 2 |
| #27160836 | 2 |
| #27160835 | 2 |
| #419×C197 | 2 |
| #1909 | 197 |