Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27161053 | C2 | semidirect |
| 3. #27160873 | C2 | semidirect |
| 4. #27160871 | C2 | semidirect |
| 5. #410×C197 | C2 | semidirect |
| 6. C2×#15691358 | C4 | semidirect |
| 7. #20263324 | C4 | semidirect |
| 9. #20263315 | C4 | semidirect |
| 16. C2×C4×Dic197 | C4 | semidirect |
| 113. C197 | #2126 | semidirect |
| 117. #410 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161625 | 2 |
| #27161053 | 2 |
| #27160873 | 2 |
| #27160871 | 2 |
| #410×C197 | 2 |
| #2126 | 197 |