Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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. #27161522 | C2 | semidirect |
| 3. C2×#20263271 | C2 | semidirect |
| 4. #27161354 | C2 | semidirect |
| 5. #27160893 | C2 | semidirect |
| 6. #27160887 | C2 | semidirect |
| 7. #350×C197 | C2 | semidirect |
| 14. C2×Dic788 | C22 | semidirect |
| 20. #20263262 | C22 | semidirect |
| 23. M32×C197 | C22 | semidirect |
| 24. C2×C16×C197 | C22 | semidirect |
| 91. C197 | #2194 | semidirect |
| 99. #350 | D197 | semidirect |
| 113. M32 | C2×D197 | semidirect |
| 114. C2×C16 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161884 | 2 |
| #27161522 | 2 |
| C2×#20263271 | 2 |
| #27161354 | 2 |
| #27160893 | 2 |
| #27160887 | 2 |
| #350×C197 | 2 |
| #2194 | 197 |