Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #31799909 | C2 | semidirect |
| 3. #31799894 | C2 | semidirect |
| 4. #31799892 | C2 | semidirect |
| 6. C4×#17984540 | C2 | semidirect |
| 7. #31799849 | C2 | semidirect |
| 8. #31799847 | C2 | semidirect |
| 9. #391×C277 | C2 | semidirect |
| 12. #22579869 | C4 | semidirect |
| 46. #17984540 | C2×C4 | semidirect |
| 47. #17984540 | C2×C4 | semidirect |
| 51. C4×Dic277 | C2×C4 | semidirect |
| 54. C2×Q8×C277 | C2×C4 | semidirect |
| 123. C277 | #2372 | semidirect |
| 127. #391 | D277 | semidirect |
| 159. C2×Q8 | C4×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579869 | 2 |
| #31799909 | 2 |
| #31799894 | 2 |
| #31799892 | 2 |
| #31799880 | 2 |
| C4×#17984540 | 2 |
| #31799849 | 2 |
| #31799847 | 2 |
| #391×C277 | 2 |
| #2372 | 277 |