Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161880 | C2 | semidirect |
| 2. #27161346 | C2 | semidirect |
| 3. #27161246 | C2 | semidirect |
| 4. #27161197 | C2 | semidirect |
| 5. #493×C197 | C2 | semidirect |
| 6. #20263371 | C22 | semidirect |
| 7. #20263352 | C22 | semidirect |
| 12. #20263332 | C22 | semidirect |
| 13. #20263262 | C22 | semidirect |
| 14. #20263254 | C22 | semidirect |
| 15. #20263243 | C22 | semidirect |
| 16. C2×D8×C197 | C22 | semidirect |
| 17. #127×C197 | C22 | semidirect |
| 18. C4×C8×C197 | C22 | semidirect |
| 23. Dic788 | D4 | semidirect |
| 24. #15691347 | D4 | semidirect |
| 26. D1576 | D4 | semidirect |
| 64. C197 | #3292 | semidirect |
| 67. #493 | D197 | semidirect |
| 77. C2×D8 | C2×D197 | semidirect |
| 79. #127 | C2×D197 | semidirect |
| 83. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161880 | 2 |
| #27161346 | 2 |
| #27161246 | 2 |
| #27161197 | 2 |
| #493×C197 | 2 |
| #3292 | 197 |