Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D197 | C2 | semidirect |
| 3. C2×#20263253 | C2 | semidirect |
| 4. C4×#15691335 | C2 | semidirect |
| 5. #27160840 | C2 | semidirect |
| 6. #27160839 | C2 | semidirect |
| 7. C2×#104×C197 | C2 | semidirect |
| 15. #20263302 | C4 | semidirect |
| 16. #20263302 | C4 | semidirect |
| 17. #20263297 | C4 | semidirect |
| 18. #20263297 | C4 | semidirect |
| 45. #15691342 | D4 | semidirect |
| 73. M16×C197 | D4 | semidirect |
| 139. C2×D197 | #104 | semidirect |
| 159. C197 | #1871 | semidirect |
| 164. C2×#104 | D197 | semidirect |
| 218. M16 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D197 | 2 |
| #27161586 | 2 |
| C2×#20263253 | 2 |
| C4×#15691335 | 2 |
| #27160840 | 2 |
| #27160839 | 2 |
| C2×#104×C197 | 2 |
| #1871 | 197 |