Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
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. #31823898 | C2 | semidirect |
| 2. C2×#22582820 | C2 | semidirect |
| 3. #31823733 | C2 | semidirect |
| 4. #31823276 | C2 | semidirect |
| 5. #31823270 | C2 | semidirect |
| 6. #31823247 | C2 | semidirect |
| 7. #576×C281 | C2 | semidirect |
| 9. C2×D2248 | C22 | semidirect |
| 13. #22582819 | C22 | semidirect |
| 14. C2×#17985113 | C22 | semidirect |
| 15. #22582815 | C22 | semidirect |
| 93. C281 | #2192 | semidirect |
| 95. #576 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31823898 | 2 |
| C2×#22582820 | 2 |
| #31823733 | 2 |
| #31823276 | 2 |
| #31823270 | 2 |
| #31823247 | 2 |
| #576×C281 | 2 |
| #2192 | 281 |