Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D547 | C2 | semidirect |
| 3. #31776034 | C2 | direct (N × H) |
| 4. C2×#22576766 | C2 | semidirect |
| 5. C2×#22576765 | C2 | semidirect |
| 6. C2×#22576763 | C2 | semidirect |
| 7. C2×#22576759 | C2 | semidirect |
| 8. C2×Q16×C547 | C2 | semidirect |
| 14. Q8×D547 | C22 | semidirect |
| 20. #22576766 | C22 | semidirect |
| 21. #22576765 | C22 | semidirect |
| 22. #22576763 | C22 | semidirect |
| 23. #22576759 | C22 | semidirect |
| 27. Q16×C547 | C22 | semidirect |
| 63. C2×C547 | #137 | semidirect |
| 67. C547 | C2×#137 | semidirect |
| 73. C2×Q16 | D547 | semidirect |
| 91. Q16 | C2×D547 | semidirect |
| 133. C2 | #31776034 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576777 | 2 |
| C2×Q8×D547 | 2 |
| #31776034 | 2 |
| C2×#22576766 | 2 |
| C2×#22576765 | 2 |
| C2×#22576763 | 2 |
| C2×#22576759 | 2 |
| C2×Q16×C547 | 2 |
| C2×#137 | 547 |