Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
270 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 73 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. #31799976 | C2 | semidirect |
| 2. #31799795 | C2 | semidirect |
| 6. #22579795 | C22 | semidirect |
| 8. C22×D4×C277 | C4 | semidirect |
| 10. #124×C277 | C4 | semidirect |
| 13. #117×C277 | C4 | semidirect |
| 69. C277 | #2128 | semidirect |
| 75. C22×D4 | Dic277 | semidirect |
| 77. #124 | Dic277 | semidirect |
| 81. #117 | Dic277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31799976 | 2 |
| #31799795 | 2 |
| #535×C277 | 2 |
| #2128 | 277 |