Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. #31799909 | C2 | semidirect |
| 5. #31799893 | C2 | semidirect |
| 6. #31799873 | C2 | semidirect |
| 7. #31799871 | C2 | semidirect |
| 8. #31799848 | C2 | semidirect |
| 9. C2×C4×Q8×C277 | C2 | semidirect |
| 12. #22579869 | C4 | semidirect |
| 43. #17984540 | C2×C4 | semidirect |
| 45. C4×Dic277 | C2×C4 | semidirect |
| 48. C2×Q8×C277 | C2×C4 | semidirect |
| 111. C277 | #2326 | semidirect |
| 114. C2×C4×Q8 | D277 | semidirect |
| 145. 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 |
| C2×C4×D1108 | 2 |
| #31799909 | 2 |
| #31799903 | 2 |
| #31799893 | 2 |
| #31799873 | 2 |
| #31799871 | 2 |
| #31799848 | 2 |
| C2×C4×Q8×C277 | 2 |
| #2326 | 277 |