Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
572 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 381 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 |
|---|---|---|
| 2. #27161035 | C2 | semidirect |
| 3. C4×#15691342 | C2 | semidirect |
| 4. C2×C4×#13096802 | C2 | semidirect |
| 6. #20263333 | C4 | direct (N × H) |
| 18. #15691342 | C2×C4 | semidirect |
| 19. C2×#13096802 | C2×C4 | semidirect |
| 48. C4×C197 | #131 | semidirect |
| 53. C197 | C4×#131 | semidirect |
| 102. C4 | #20263333 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263333 | 2 |
| #27161035 | 2 |
| C4×#15691342 | 2 |
| C2×C4×#13096802 | 2 |
| C4×#41×C197 | 2 |
| C4×#131 | 197 |