Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. #31800437 | C2 | semidirect |
| 2. C2×#22579821 | C2 | semidirect |
| 3. #31800272 | C2 | semidirect |
| 4. #31799815 | C2 | semidirect |
| 5. #31799809 | C2 | semidirect |
| 6. #31799786 | C2 | semidirect |
| 7. #576×C277 | C2 | semidirect |
| 9. C2×D2216 | C22 | semidirect |
| 13. #22579820 | C22 | semidirect |
| 14. C2×#17984538 | C22 | semidirect |
| 15. #22579816 | C22 | semidirect |
| 93. C277 | #2192 | semidirect |
| 95. #576 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800437 | 2 |
| C2×#22579821 | 2 |
| #31800272 | 2 |
| #31799815 | 2 |
| #31799809 | 2 |
| #31799786 | 2 |
| #576×C277 | 2 |
| #2192 | 277 |