Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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. #31800020 | C2 | semidirect |
| 3. #31800019 | C2 | semidirect |
| 4. #31799999 | C2 | semidirect |
| 5. #31799975 | C2 | semidirect |
| 6. #31799968 | C2 | semidirect |
| 7. #416×C277 | C2 | semidirect |
| 10. #22579927 | C4 | semidirect |
| 12. #22579926 | C4 | semidirect |
| 20. C2×#17984547 | C22 | semidirect |
| 21. #22579839 | C22 | semidirect |
| 29. C22×C8×C277 | C22 | semidirect |
| 30. #117×C277 | C22 | semidirect |
| 166. C277 | #1794 | semidirect |
| 172. #416 | D277 | semidirect |
| 189. C22×C8 | C2×D277 | semidirect |
| 191. #117 | C2×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800838 | 2 |
| #31800020 | 2 |
| #31800019 | 2 |
| #31799999 | 2 |
| #31799975 | 2 |
| #31799968 | 2 |
| #416×C277 | 2 |
| #1794 | 277 |