Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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. #27161814 | C2 | semidirect |
| 2. #27161436 | C2 | semidirect |
| 3. #27161427 | C2 | semidirect |
| 4. #27161376 | C2 | semidirect |
| 5. #27161371 | C2 | semidirect |
| 6. #27161294 | C2 | semidirect |
| 8. Q8×#13096802 | C2 | semidirect |
| 9. C4×#15691346 | C2 | semidirect |
| 10. C4×#15691343 | C2 | semidirect |
| 11. #554×C197 | C2 | semidirect |
| 122. C197 | #3361 | semidirect |
| 125. #554 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161814 | 2 |
| #27161436 | 2 |
| #27161427 | 2 |
| #27161376 | 2 |
| #27161371 | 2 |
| #27161294 | 2 |
| #27161274 | 2 |
| Q8×#13096802 | 2 |
| C4×#15691346 | 2 |
| C4×#15691343 | 2 |
| #554×C197 | 2 |
| #3361 | 197 |