Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31800038 | C2 | semidirect |
| 3. #31800018 | C2 | semidirect |
| 4. #31799976 | C2 | semidirect |
| 5. #31799975 | C2 | semidirect |
| 6. #31799960 | C2 | semidirect |
| 7. #421×C277 | C2 | semidirect |
| 13. C2×#17984553 | C4 | semidirect |
| 14. C2×#17984551 | C4 | semidirect |
| 15. C2×#17984550 | C4 | semidirect |
| 16. C2×#17984548 | C4 | semidirect |
| 132. C277 | #1976 | semidirect |
| 137. #421 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579900 | 2 |
| #31800038 | 2 |
| #31800018 | 2 |
| #31799976 | 2 |
| #31799975 | 2 |
| #31799960 | 2 |
| #421×C277 | 2 |
| #1976 | 277 |