Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
310 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 155 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. #31775967 | C2 | semidirect |
| 3. #31775964 | C2 | semidirect |
| 4. (C22⋊D547)⋊C4 | C2 | semidirect |
| 5. #31775959 | C2 | semidirect |
| 6. C2×C4×Dic547 | C2 | semidirect |
| 7. C42×D547 | C2 | semidirect |
| 8. #117×C547 | C2 | semidirect |
| 9. #22576776 | C4 | semidirect |
| 27. Dic1094 | C2×C4 | semidirect |
| 28. D2188 | C2×C4 | semidirect |
| 29. C22⋊D547 | C2×C4 | semidirect |
| 35. C4×D547 | C2×C4 | semidirect |
| 37. C2×C4×C547 | C2×C4 | semidirect |
| 51. Dic547 | #41 | semidirect |
| 56. C547 | C4×#41 | semidirect |
| 63. #117 | D547 | semidirect |
| 94. C2×C4 | C4×D547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576776 | 2 |
| #31775967 | 2 |
| #31775964 | 2 |
| (C22⋊D547)⋊C4 | 2 |
| #31775959 | 2 |
| C2×C4×Dic547 | 2 |
| C42×D547 | 2 |
| #117×C547 | 2 |
| C4×#41 | 547 |