Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 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. #27161635 | C2 | direct (N × H) |
| 2. C2×#20263325 | C2 | semidirect |
| 3. C2×#20263318 | C2 | semidirect |
| 5. C2×#20263291 | C2 | semidirect |
| 8. C2×#125×C197 | C2 | semidirect |
| 12. #20263325 | C22 | semidirect |
| 13. #20263318 | C22 | semidirect |
| 15. #20263291 | C22 | semidirect |
| 25. #125×C197 | C22 | semidirect |
| 36. C2×C4×D197 | Q8 | semidirect |
| 63. C4×D197 | C2×Q8 | semidirect |
| 83. C2×C197 | #533 | semidirect |
| 87. C197 | C2×#533 | semidirect |
| 92. C2×#125 | D197 | semidirect |
| 102. #125 | C2×D197 | semidirect |
| 172. C2 | #27161635 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161635 | 2 |
| C2×#20263325 | 2 |
| C2×#20263318 | 2 |
| C2×#20263304 | 2 |
| C2×#20263291 | 2 |
| C2×#20263284 | 2 |
| C2×C42×D197 | 2 |
| C2×#125×C197 | 2 |
| C2×#533 | 197 |