Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C4×Dic394 | C2 | semidirect |
| 3. #27161415 | C2 | semidirect |
| 5. #27161387 | C2 | semidirect |
| 6. #27161302 | C2 | semidirect |
| 7. #27161237 | C2 | semidirect |
| 9. #27161187 | C2 | semidirect |
| 10. #27161181 | C2 | semidirect |
| 11. #432×C197 | C2 | semidirect |
| 131. C197 | #3117 | semidirect |
| 143. #432 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161613 | 2 |
| C2×C4×Dic394 | 2 |
| #27161415 | 2 |
| #27161398 | 2 |
| #27161387 | 2 |
| #27161302 | 2 |
| #27161237 | 2 |
| #27161220 | 2 |
| #27161187 | 2 |
| #27161181 | 2 |
| #432×C197 | 2 |
| #3117 | 197 |