Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#20263346 | C2 | semidirect |
| 2. #27161734 | C2 | semidirect |
| 3. #27161451 | C2 | semidirect |
| 4. #27161306 | C2 | semidirect |
| 5. #27161289 | C2 | semidirect |
| 6. #27161271 | C2 | semidirect |
| 7. #27161241 | C2 | semidirect |
| 8. #27161222 | C2 | semidirect |
| 9. C4×#15691345 | C2 | semidirect |
| 10. D4×#13096802 | C2 | semidirect |
| 11. #550×C197 | C2 | semidirect |
| 52. #15691345 | D4 | semidirect |
| 129. C4×C197 | #135 | semidirect |
| 140. C197 | #3284 | semidirect |
| 143. #550 | D197 | semidirect |
| 272. C4 | #20263346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263346 | 2 |
| #27161734 | 2 |
| #27161451 | 2 |
| #27161306 | 2 |
| #27161289 | 2 |
| #27161271 | 2 |
| #27161241 | 2 |
| #27161222 | 2 |
| C4×#15691345 | 2 |
| D4×#13096802 | 2 |
| #550×C197 | 2 |
| #3284 | 197 |