Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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. M32×D197 | C2 | semidirect |
| 3. #106×D197 | C2 | semidirect |
| 4. #27160890 | C2 | semidirect |
| 5. #27160889 | C2 | semidirect |
| 6. #27160888 | C2 | semidirect |
| 7. #360×C197 | C2 | semidirect |
| 9. #20263349 | C4 | semidirect |
| 13. #20263345 | C4 | semidirect |
| 14. Q16×D197 | C4 | semidirect |
| 16. D8×D197 | C4 | semidirect |
| 19. #20263266 | C22 | semidirect |
| 22. #20263258 | C22 | semidirect |
| 25. M32×C197 | C22 | semidirect |
| 26. #106×C197 | C22 | semidirect |
| 38. Dic788 | C2×C4 | semidirect |
| 43. D1576 | C2×C4 | semidirect |
| 54. Q16×C197 | C2×C4 | semidirect |
| 56. D8×C197 | C2×C4 | semidirect |
| 110. D197 | #360 | direct (N × H) |
| 111. C197 | C2×#360 | semidirect |
| 119. #360 | D197 | direct (N × H) |
| 134. M32 | C2×D197 | semidirect |
| 138. #106 | C2×D197 | semidirect |
| 153. Q16 | C4×D197 | semidirect |
| 160. D8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D197 | 2 |
| M32×D197 | 2 |
| #106×D197 | 2 |
| #27160890 | 2 |
| #27160889 | 2 |
| #27160888 | 2 |
| #360×C197 | 2 |
| C2×#360 | 197 |