Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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. #27161562 | C2 | semidirect |
| 3. #27161089 | C2 | semidirect |
| 4. #27161081 | C2 | semidirect |
| 5. #27161076 | C2 | semidirect |
| 6. C2×#20263251 | C2 | semidirect |
| 7. C2×#131×C197 | C2 | semidirect |
| 9. #20263373 | C4 | semidirect |
| 28. #15691358 | C2×C4 | semidirect |
| 32. C2×Dic394 | C2×C4 | semidirect |
| 94. C197 | #2898 | semidirect |
| 97. C2×#131 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263373 | 2 |
| #27161562 | 2 |
| #27161089 | 2 |
| #27161081 | 2 |
| #27161076 | 2 |
| C2×#20263251 | 2 |
| C2×#131×C197 | 2 |
| #2898 | 197 |