Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×D4×Dic197 | C2 | semidirect |
| 3. C2×#20263288 | C2 | semidirect |
| 4. #27161159 | C2 | direct (N × H) |
| 5. C2×#20263259 | C2 | semidirect |
| 6. C2×#20263248 | C2 | semidirect |
| 7. C2×C8×Dic197 | C2 | semidirect |
| 8. C2×#102×C197 | C2 | semidirect |
| 12. C2×#15691343 | C4 | semidirect |
| 16. D4×Dic197 | C22 | semidirect |
| 18. #20263288 | C22 | semidirect |
| 23. #20263259 | C22 | semidirect |
| 24. #20263248 | C22 | semidirect |
| 25. C8×Dic197 | C22 | semidirect |
| 29. #102×C197 | C22 | semidirect |
| 33. C2×D788 | C2×C4 | semidirect |
| 42. #15691343 | C2×C4 | semidirect |
| 43. C2×#13096802 | C2×C4 | semidirect |
| 54. C2×D4×C197 | C2×C4 | semidirect |
| 68. D788 | C22×C4 | semidirect |
| 73. C2×Dic197 | D8 | semidirect |
| 77. #13096802 | C22×C4 | semidirect |
| 85. D4×C197 | C22×C4 | semidirect |
| 111. Dic197 | C2×D8 | semidirect |
| 113. C2×C197 | C4×D8 | semidirect |
| 118. C197 | C2×C4×D8 | semidirect |
| 126. C2×#102 | D197 | semidirect |
| 147. #102 | C2×D197 | semidirect |
| 157. C2×D4 | C4×D197 | semidirect |
| 195. D4 | C2×C4×D197 | semidirect |
| 233. C2 | #27161159 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691343 | 2 |
| C2×D4×Dic197 | 2 |
| C2×#20263288 | 2 |
| #27161159 | 2 |
| C2×#20263259 | 2 |
| C2×#20263248 | 2 |
| C2×C8×Dic197 | 2 |
| C2×#102×C197 | 2 |
| C2×C4×D8 | 197 |