Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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×#20263349 | C2 | semidirect |
| 2. C2×M16×D197 | C2 | semidirect |
| 3. #27161592 | C2 | semidirect |
| 4. #27161334 | C2 | semidirect |
| 5. #27161333 | C2 | semidirect |
| 6. #27161332 | C2 | semidirect |
| 7. #27161328 | C2 | semidirect |
| 8. #27161327 | C2 | semidirect |
| 9. #27161114 | C2 | semidirect |
| 10. #27161074 | C2 | semidirect |
| 11. #470×C197 | C2 | semidirect |
| 15. C2×#15691345 | C22 | semidirect |
| 16. C2×D1576 | C22 | semidirect |
| 31. #20263259 | C22 | semidirect |
| 32. #20263258 | C22 | semidirect |
| 33. #20263250 | C22 | semidirect |
| 34. #20263248 | C22 | semidirect |
| 35. #20263246 | C22 | semidirect |
| 36. C2×Q16×C197 | C22 | semidirect |
| 39. #106×C197 | C22 | semidirect |
| 40. #103×C197 | C22 | semidirect |
| 64. C8×D197 | D4 | semidirect |
| 140. C197 | #3054 | semidirect |
| 146. #470 | D197 | semidirect |
| 156. C2×Q16 | C2×D197 | semidirect |
| 177. #106 | C2×D197 | semidirect |
| 179. #103 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263349 | 2 |
| C2×M16×D197 | 2 |
| #27161592 | 2 |
| #27161334 | 2 |
| #27161333 | 2 |
| #27161332 | 2 |
| #27161328 | 2 |
| #27161327 | 2 |
| #27161114 | 2 |
| #27161074 | 2 |
| #470×C197 | 2 |
| #3054 | 197 |