Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
216 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C4×#15691333 | C2 | semidirect |
| 4. C16×Dic197 | C2 | semidirect |
| 5. C4×C16×C197 | C2 | semidirect |
| 10. C16×D197 | C4 | direct (N × H) |
| 24. #15691333 | C2×C4 | semidirect |
| 28. C16×C197 | C2×C4 | semidirect |
| 32. C4×D197 | C16 | direct (N × H) |
| 44. C4×C197 | C2×C16 | semidirect |
| 48. Dic197 | C2×C16 | semidirect |
| 51. D197 | C4×C16 | direct (N × H) |
| 52. C197 | C2×C4×C16 | semidirect |
| 58. C4×C16 | D197 | direct (N × H) |
| 81. C16 | C4×D197 | direct (N × H) |
| 99. C4 | C16×D197 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D197 | 2 |
| C4×C8×D197 | 2 |
| C4×#15691333 | 2 |
| C16×Dic197 | 2 |
| C4×C16×C197 | 2 |
| C2×C4×C16 | 197 |