Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
132 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 51 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. C4×D2188 | C2 | semidirect |
| 3. #31775933 | C2 | semidirect |
| 4. #31775923 | C2 | semidirect |
| 5. #31775922 | C2 | semidirect |
| 6. #31775913 | C2 | semidirect |
| 7. C4×D4×C547 | C2 | semidirect |
| 10. #22576761 | C4 | semidirect |
| 22. D2188 | C2×C4 | semidirect |
| 26. C547⋊C8 | C2×C4 | semidirect |
| 29. D4×C547 | C2×C4 | semidirect |
| 53. C547 | #442 | semidirect |
| 57. C4×D4 | D547 | semidirect |
| 79. D4 | C4×D547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576761 | 2 |
| C4×D2188 | 2 |
| #31775933 | 2 |
| #31775923 | 2 |
| #31775922 | 2 |
| #31775913 | 2 |
| C4×D4×C547 | 2 |
| #442 | 547 |