Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 1. #27161750 | C2 | semidirect |
| 2. D4×Dic394 | C2 | semidirect |
| 3. #27161426 | C2 | semidirect |
| 4. #27161424 | C2 | semidirect |
| 5. #27161359 | C2 | semidirect |
| 6. #27161358 | C2 | semidirect |
| 7. #27161274 | C2 | semidirect |
| 8. #27161272 | C2 | semidirect |
| 9. C8×Dic394 | C2 | semidirect |
| 10. #27161159 | C2 | semidirect |
| 11. C4×D8×C197 | C2 | semidirect |
| 78. Dic394 | D8 | semidirect |
| 96. D4×C197 | #41 | semidirect |
| 131. C197 | #3358 | semidirect |
| 143. C4×D8 | D197 | semidirect |
| 222. D4 | #15691358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161750 | 2 |
| D4×Dic394 | 2 |
| #27161426 | 2 |
| #27161424 | 2 |
| #27161359 | 2 |
| #27161358 | 2 |
| #27161274 | 2 |
| #27161272 | 2 |
| C8×Dic394 | 2 |
| #27161159 | 2 |
| C4×D8×C197 | 2 |
| #3358 | 197 |