Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #27211765 | C2 | semidirect |
| 2. #27211764 | C2 | semidirect |
| 3. #27211751 | C2 | semidirect |
| 4. #27211746 | C2 | semidirect |
| 5. #27211740 | C2 | semidirect |
| 6. C2×#20269400 | C2 | semidirect |
| 7. #131×C419 | C2 | semidirect |
| 10. #20269411 | C22 | semidirect |
| 12. C2×Dic838 | C22 | semidirect |
| 16. Dic1676 | C22 | semidirect |
| 17. #20269400 | C22 | semidirect |
| 18. #20269400 | C22 | semidirect |
| 19. #20269400 | C22 | semidirect |
| 20. D3352 | C22 | semidirect |
| 22. M16×C419 | C22 | semidirect |
| 23. C2×C8×C419 | C22 | semidirect |
| 53. C419 | #577 | semidirect |
| 61. #131 | D419 | semidirect |
| 76. M16 | C2×D419 | semidirect |
| 77. C2×C8 | C2×D419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27211765 | 2 |
| #27211764 | 2 |
| #27211751 | 2 |
| #27211746 | 2 |
| #27211740 | 2 |
| C2×#20269400 | 2 |
| #131×C419 | 2 |
| #577 | 419 |