Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. C2×#20264355 | C2 | semidirect |
| 3. C2×#20264354 | C2 | semidirect |
| 4. #27165717 | C2 | semidirect |
| 5. #27165657 | C2 | semidirect |
| 6. #27165649 | C2 | semidirect |
| 7. #102×C401 | C2 | semidirect |
| 9. C2×Dic802 | C22 | semidirect |
| 17. C2×#15691999 | C22 | semidirect |
| 21. C2×C8×C401 | C22 | semidirect |
| 22. C4⋊C4×C401 | C22 | semidirect |
| 54. C2×D401 | SD16 | semidirect |
| 66. C401 | #450 | semidirect |
| 73. #102 | D401 | semidirect |
| 86. C2×C8 | C2×D401 | semidirect |
| 88. C4⋊C4 | C2×D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D401 | 2 |
| C2×#20264355 | 2 |
| C2×#20264354 | 2 |
| #27165717 | 2 |
| #27165657 | 2 |
| #27165649 | 2 |
| #102×C401 | 2 |
| #450 | 401 |