Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
168 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 63 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. #31800129 | C2 | semidirect |
| 4. #31799732 | C2 | semidirect |
| 6. #31799724 | C2 | semidirect |
| 7. #334×C277 | C2 | semidirect |
| 53. #14555660 | SD16 | semidirect |
| 77. C277 | #1582 | semidirect |
| 82. #334 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800129 | 2 |
| C4×#17984552 | 2 |
| #31800067 | 2 |
| #31799732 | 2 |
| #31799729 | 2 |
| #31799724 | 2 |
| #334×C277 | 2 |
| #1582 | 277 |