Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161035 | C2 | semidirect |
| 4. C2×C8×Dic197 | C2 | semidirect |
| 5. #27160844 | C2 | semidirect |
| 6. #27160838 | C2 | semidirect |
| 9. #20263333 | C4 | semidirect |
| 16. #20263253 | C4 | semidirect |
| 23. #103×C197 | C4 | semidirect |
| 24. #102×C197 | C4 | semidirect |
| 98. C197 | #1764 | semidirect |
| 119. #103 | Dic197 | semidirect |
| 120. #102 | Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263333 | 2 |
| C2×#20263253 | 2 |
| #27161035 | 2 |
| C2×C8×Dic197 | 2 |
| #27160844 | 2 |
| #27160838 | 2 |
| #416×C197 | 2 |
| #1764 | 197 |