Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 83 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. #27161102 | C2 | semidirect |
| 3. C2×#20263254 | C2 | semidirect |
| 4. C2×#20263253 | C2 | semidirect |
| 5. C2×#20263252 | C2 | semidirect |
| 6. #27160925 | C2 | semidirect |
| 7. C2×#104×C197 | C2 | semidirect |
| 10. #20263324 | C4 | semidirect |
| 11. #20263322 | C4 | semidirect |
| 12. #20263315 | C4 | semidirect |
| 13. #20263313 | C4 | semidirect |
| 48. C4×Dic197 | D4 | semidirect |
| 63. C42×C197 | D4 | semidirect |
| 125. C197 | #1963 | semidirect |
| 132. C2×#104 | D197 | semidirect |
| 189. C42 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161625 | 2 |
| #27161102 | 2 |
| C2×#20263254 | 2 |
| C2×#20263253 | 2 |
| C2×#20263252 | 2 |
| #27160925 | 2 |
| C2×#104×C197 | 2 |
| #1963 | 197 |