Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
616 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×D1576 | C2 | semidirect |
| 2. C22×C8×D197 | C2 | semidirect |
| 3. C2×#20263301 | C2 | semidirect |
| 4. #27161316 | C2 | direct (N × H) |
| 5. C2×#20263246 | C2 | semidirect |
| 6. C2×#107×C197 | C2 | semidirect |
| 11. C2×D1576 | C22 | semidirect |
| 14. C2×C8×D197 | C22 | semidirect |
| 16. #20263301 | C22 | semidirect |
| 18. #20263246 | C22 | semidirect |
| 21. #107×C197 | C22 | semidirect |
| 42. C2×C8×C197 | D4 | semidirect |
| 52. C22×D197 | D8 | semidirect |
| 71. C8×C197 | C2×D4 | semidirect |
| 83. C2×D197 | C2×D8 | semidirect |
| 89. C2×C197 | #466 | semidirect |
| 95. C197 | C2×#466 | semidirect |
| 101. C2×#107 | D197 | semidirect |
| 116. #107 | C2×D197 | semidirect |
| 137. C2×C8 | D788 | semidirect |
| 167. C8 | C2×D788 | semidirect |
| 187. C2 | #27161316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1576 | 2 |
| C22×C8×D197 | 2 |
| C2×#20263301 | 2 |
| #27161316 | 2 |
| C2×#20263246 | 2 |
| C2×#107×C197 | 2 |
| C2×#466 | 197 |