Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. Q8×Dic394 | C2 | semidirect |
| 3. #27161426 | C2 | semidirect |
| 4. #27161424 | C2 | semidirect |
| 5. #27161369 | C2 | semidirect |
| 6. #27161368 | C2 | semidirect |
| 7. #27161279 | C2 | semidirect |
| 8. #27161277 | C2 | semidirect |
| 9. C8×Dic394 | C2 | semidirect |
| 10. #27161164 | C2 | semidirect |
| 11. C4×SD16×C197 | C2 | semidirect |
| 77. Dic394 | SD16 | semidirect |
| 91. Q8×C197 | #41 | semidirect |
| 125. C197 | #3362 | semidirect |
| 137. C4×SD16 | D197 | semidirect |
| 206. Q8 | #15691358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic394 | 2 |
| #27161750 | 2 |
| #27161426 | 2 |
| #27161424 | 2 |
| #27161369 | 2 |
| #27161368 | 2 |
| #27161279 | 2 |
| #27161277 | 2 |
| C8×Dic394 | 2 |
| #27161164 | 2 |
| C4×SD16×C197 | 2 |
| #3362 | 197 |