Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 565 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. #27161705 | C2 | direct (N × H) |
| 2. C2×#20263305 | C2 | semidirect |
| 3. C2×#20263303 | C2 | semidirect |
| 6. C22×Dic394 | C22 | semidirect |
| 8. #20263305 | C22 | semidirect |
| 9. #20263303 | C22 | semidirect |
| 10. C2×C4⋊Dic197 | C22 | semidirect |
| 11. C2×#15691337 | C22 | semidirect |
| 20. C2×Dic394 | C23 | semidirect |
| 24. C4⋊Dic197 | C23 | semidirect |
| 25. #15691337 | C23 | semidirect |
| 29. C24×C197 | Q8 | semidirect |
| 47. C23×C197 | C2×Q8 | semidirect |
| 68. C2×C197 | #543 | semidirect |
| 71. C197 | C2×#543 | semidirect |
| 92. C24 | Dic394 | semidirect |
| 115. C23 | C2×Dic394 | semidirect |
| 140. C2 | #27161705 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161705 | 2 |
| C2×#20263305 | 2 |
| C2×#20263303 | 2 |
| C22×C22⋊Dic197 | 2 |
| C22×C22⋊C4×C197 | 2 |
| C2×#543 | 197 |