Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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×Q16×D197 | C2 | semidirect |
| 4. #27161458 | C2 | semidirect |
| 5. #27161319 | C2 | semidirect |
| 6. #27161290 | C2 | semidirect |
| 7. #27161236 | C2 | semidirect |
| 8. #27161233 | C2 | semidirect |
| 9. C4×#15691348 | C2 | semidirect |
| 11. #462×C197 | C2 | semidirect |
| 57. #15691348 | D4 | semidirect |
| 89. D788 | Q16 | semidirect |
| 114. C2×D197 | C2×Q16 | semidirect |
| 119. C4×C197 | C2×Q16 | semidirect |
| 130. C197 | D4×Q16 | semidirect |
| 138. #462 | D197 | semidirect |
| 254. C4 | Q16×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D197 | 2 |
| Q8×D788 | 2 |
| #27161744 | 2 |
| #27161458 | 2 |
| #27161319 | 2 |
| #27161290 | 2 |
| #27161236 | 2 |
| #27161233 | 2 |
| C4×#15691348 | 2 |
| #27161144 | 2 |
| #462×C197 | 2 |
| D4×Q16 | 197 |