Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #31776050 | C2 | semidirect |
| 2. #31776049 | C2 | semidirect |
| 3. #31776035 | C2 | semidirect |
| 4. #31776034 | C2 | semidirect |
| 5. #31776031 | C2 | semidirect |
| 6. #31776023 | C2 | semidirect |
| 7. #31776022 | C2 | semidirect |
| 8. C2×#22576766 | C2 | semidirect |
| 9. Q16×D547 | C2 | semidirect |
| 10. #31776010 | C2 | semidirect |
| 11. #137×C547 | C2 | semidirect |
| 87. C547 | #578 | semidirect |
| 94. #137 | D547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31776050 | 2 |
| #31776049 | 2 |
| #31776035 | 2 |
| #31776034 | 2 |
| #31776031 | 2 |
| #31776023 | 2 |
| #31776022 | 2 |
| C2×#22576766 | 2 |
| Q16×D547 | 2 |
| #31776010 | 2 |
| #137×C547 | 2 |
| #578 | 547 |