Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 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×C8×D409 | C2 | semidirect |
| 3. C4⋊C4×D409 | C2 | semidirect |
| 4. #27189639 | C2 | semidirect |
| 5. #27189638 | C2 | semidirect |
| 6. #27189637 | C2 | semidirect |
| 7. #102×C409 | C2 | semidirect |
| 12. D4×D409 | C4 | semidirect |
| 15. C2×#15692543 | C22 | semidirect |
| 17. C4⋊Dic409 | C22 | semidirect |
| 20. C2×C8×C409 | C22 | semidirect |
| 21. C4⋊C4×C409 | C22 | semidirect |
| 28. D1636 | C2×C4 | semidirect |
| 38. D4×C409 | C2×C4 | semidirect |
| 63. D409 | #102 | direct (N × H) |
| 64. C409 | C2×#102 | semidirect |
| 72. #102 | D409 | direct (N × H) |
| 83. C2×C8 | C2×D409 | semidirect |
| 86. C4⋊C4 | C2×D409 | semidirect |
| 97. D4 | C4×D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D409 | 2 |
| C2×C8×D409 | 2 |
| C4⋊C4×D409 | 2 |
| #27189639 | 2 |
| #27189638 | 2 |
| #27189637 | 2 |
| #102×C409 | 2 |
| C2×#102 | 409 |