Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 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 |
|---|---|---|
| 1. C2×#20266973 | C2 | semidirect |
| 2. C22×#15692543 | C2 | semidirect |
| 3. #27189691 | C2 | semidirect |
| 4. #27189650 | C2 | semidirect |
| 5. #27189638 | C2 | semidirect |
| 6. #27189637 | C2 | semidirect |
| 7. #121×C409 | C2 | semidirect |
| 27. #15692543 | D4 | semidirect |
| 43. C22×C409 | D8 | semidirect |
| 59. C409 | #466 | semidirect |
| 64. #121 | D409 | semidirect |
| 106. C22 | #20266973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20266973 | 2 |
| C22×#15692543 | 2 |
| #27189691 | 2 |
| #27189650 | 2 |
| #27189638 | 2 |
| #27189637 | 2 |
| #121×C409 | 2 |
| #466 | 409 |