Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#20263333 | C2 | semidirect |
| 2. #27161201 | C2 | semidirect |
| 3. #27161196 | C2 | semidirect |
| 4. #27161128 | C2 | semidirect |
| 5. #27161096 | C2 | semidirect |
| 6. #27161037 | C2 | semidirect |
| 10. #20263333 | C22 | semidirect |
| 11. #20263333 | C22 | semidirect |
| 17. #20263262 | C22 | semidirect |
| 18. #20263253 | C22 | semidirect |
| 19. #20263236 | C22 | semidirect |
| 20. C8×Dic197 | C22 | semidirect |
| 22. #137×C197 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C197 | C4 | semidirect |
| 89. C197 | #2955 | semidirect |
| 99. #137 | Dic197 | semidirect |
| 100. AGL(1,ℤ/8) | Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263333 | 2 |
| #27161201 | 2 |
| #27161196 | 2 |
| #27161128 | 2 |
| #27161096 | 2 |
| #27161037 | 2 |
| #575×C197 | 2 |
| #2955 | 197 |