Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 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×#20264366 | C2 | semidirect |
| 2. #27165757 | C2 | direct (N × H) |
| 3. C2×#20264356 | C2 | semidirect |
| 4. C2×#20264354 | C2 | semidirect |
| 5. C2×#20264353 | C2 | semidirect |
| 6. C2×#20264351 | C2 | semidirect |
| 7. C22×#15691999 | C2 | semidirect |
| 8. C2×#41×C401 | C2 | semidirect |
| 10. #20264366 | C22 | semidirect |
| 15. #20264356 | C22 | semidirect |
| 16. #20264354 | C22 | semidirect |
| 17. #20264353 | C22 | semidirect |
| 18. #20264351 | C22 | semidirect |
| 21. C2×#15691999 | C22 | semidirect |
| 23. #41×C401 | C22 | semidirect |
| 66. C2×C401 | #135 | semidirect |
| 69. C401 | C2×#135 | semidirect |
| 72. C2×#41 | D401 | semidirect |
| 82. #41 | C2×D401 | semidirect |
| 137. C2 | #27165757 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264366 | 2 |
| #27165757 | 2 |
| C2×#20264356 | 2 |
| C2×#20264354 | 2 |
| C2×#20264353 | 2 |
| C2×#20264351 | 2 |
| C22×#15691999 | 2 |
| C2×#41×C401 | 2 |
| C2×#135 | 401 |