Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 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 |
|---|---|---|
| 1. C2×#20264367 | C2 | semidirect |
| 2. C2×#20264365 | C2 | semidirect |
| 3. #27165758 | C2 | direct (N × H) |
| 4. C2×#20264356 | C2 | semidirect |
| 5. C2×#20264355 | C2 | semidirect |
| 6. C2×#20264351 | C2 | semidirect |
| 7. C2×C8×D401 | C2 | semidirect |
| 8. C2×SD16×C401 | C2 | semidirect |
| 10. #20264367 | C22 | semidirect |
| 12. #20264365 | C22 | semidirect |
| 20. #20264356 | C22 | semidirect |
| 21. #20264355 | C22 | semidirect |
| 22. #20264351 | C22 | semidirect |
| 24. C8×D401 | C22 | semidirect |
| 27. SD16×C401 | C22 | semidirect |
| 65. C2×C401 | #135 | semidirect |
| 69. C401 | C2×#135 | semidirect |
| 76. C2×SD16 | D401 | semidirect |
| 94. SD16 | C2×D401 | semidirect |
| 137. C2 | #27165758 | 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×#20264365 | 2 |
| #27165758 | 2 |
| C2×#20264356 | 2 |
| C2×#20264355 | 2 |
| C2×#20264351 | 2 |
| C2×C8×D401 | 2 |
| C2×SD16×C401 | 2 |
| C2×#135 | 401 |