Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #27189748 | C2 | semidirect |
| 3. #27189723 | C2 | semidirect |
| 4. #27189653 | C2 | semidirect |
| 5. #27189636 | C2 | semidirect |
| 6. #27189634 | C2 | semidirect |
| 7. C2×SD16×C409 | C2 | semidirect |
| 51. C409 | #471 | semidirect |
| 55. C2×SD16 | D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27189748 | 2 |
| #27189743 | 2 |
| #27189723 | 2 |
| #27189653 | 2 |
| #27189636 | 2 |
| #27189634 | 2 |
| C2×SD16×C409 | 2 |
| #471 | 409 |