Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D401 | C2 | semidirect |
| 3. #27165769 | C2 | direct (N × H) |
| 4. C2×#20264356 | C2 | semidirect |
| 5. C2×#20264355 | C2 | semidirect |
| 6. C2×#20264353 | C2 | semidirect |
| 7. C2×#20264349 | C2 | semidirect |
| 8. C2×Q16×C401 | C2 | semidirect |
| 14. Q8×D401 | C22 | semidirect |
| 20. #20264356 | C22 | semidirect |
| 21. #20264355 | C22 | semidirect |
| 22. #20264353 | C22 | semidirect |
| 23. #20264349 | C22 | semidirect |
| 27. Q16×C401 | C22 | semidirect |
| 63. C2×C401 | #137 | semidirect |
| 67. C401 | C2×#137 | semidirect |
| 73. C2×Q16 | D401 | semidirect |
| 91. Q16 | C2×D401 | semidirect |
| 133. C2 | #27165769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264367 | 2 |
| C2×Q8×D401 | 2 |
| #27165769 | 2 |
| C2×#20264356 | 2 |
| C2×#20264355 | 2 |
| C2×#20264353 | 2 |
| C2×#20264349 | 2 |
| C2×Q16×C401 | 2 |
| C2×#137 | 401 |