Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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. #27161187 | C2 | semidirect |
| 4. #27161186 | C2 | semidirect |
| 5. #27161185 | C2 | semidirect |
| 6. C4×#15691348 | C2 | semidirect |
| 7. #27161171 | C2 | semidirect |
| 11. #441×C197 | C2 | semidirect |
| 15. Q16×D197 | C4 | semidirect |
| 108. C197 | #2950 | semidirect |
| 115. #441 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D197 | 2 |
| #27161555 | 2 |
| #27161187 | 2 |
| #27161186 | 2 |
| #27161185 | 2 |
| C4×#15691348 | 2 |
| #27161171 | 2 |
| #27161114 | 2 |
| #27161086 | 2 |
| #27161036 | 2 |
| #441×C197 | 2 |
| #2950 | 197 |