Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D277 | C2 | semidirect |
| 3. C2×#22579807 | C2 | semidirect |
| 4. C4×#17984540 | C2 | semidirect |
| 5. #31799763 | C2 | semidirect |
| 6. #31799762 | C2 | semidirect |
| 7. C2×#104×C277 | C2 | semidirect |
| 15. #22579856 | C4 | semidirect |
| 16. #22579856 | C4 | semidirect |
| 17. #22579851 | C4 | semidirect |
| 18. #22579851 | C4 | semidirect |
| 45. #17984547 | D4 | semidirect |
| 73. M16×C277 | D4 | semidirect |
| 139. C2×D277 | #104 | semidirect |
| 159. C277 | #1871 | semidirect |
| 164. C2×#104 | D277 | semidirect |
| 218. M16 | C22⋊D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D277 | 2 |
| #31800509 | 2 |
| C2×#22579807 | 2 |
| C4×#17984540 | 2 |
| #31799763 | 2 |
| #31799762 | 2 |
| C2×#104×C277 | 2 |
| #1871 | 277 |