Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 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×#20266971 | C2 | semidirect |
| 3. #27189697 | C2 | semidirect |
| 5. #27189640 | C2 | semidirect |
| 6. #27189637 | C2 | semidirect |
| 7. #107×C409 | C2 | semidirect |
| 36. C8×C409 | D4 | semidirect |
| 55. C409 | #468 | semidirect |
| 61. #107 | D409 | semidirect |
| 92. C8 | D1636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20266977 | 2 |
| C2×#20266971 | 2 |
| #27189697 | 2 |
| #27189692 | 2 |
| #27189640 | 2 |
| #27189637 | 2 |
| #107×C409 | 2 |
| #468 | 409 |