Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
128 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 41 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×#20266977 | C2 | semidirect |
| 2. C2×#20266976 | C2 | semidirect |
| 4. #27189682 | C2 | semidirect |
| 5. #27189646 | C2 | semidirect |
| 6. #27189637 | C2 | semidirect |
| 7. #102×C409 | C2 | semidirect |
| 23. Dic818 | D4 | semidirect |
| 50. Dic409 | SD16 | semidirect |
| 56. C409 | #460 | semidirect |
| 64. #102 | D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20266977 | 2 |
| C2×#20266976 | 2 |
| #27189713 | 2 |
| #27189682 | 2 |
| #27189646 | 2 |
| #27189637 | 2 |
| #102×C409 | 2 |
| #460 | 409 |