Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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×#22582822 | C2 | semidirect |
| 3. #31823735 | C2 | semidirect |
| 4. #31823277 | C2 | semidirect |
| 5. #31823270 | C2 | semidirect |
| 6. #31823248 | C2 | semidirect |
| 7. #510×C281 | C2 | semidirect |
| 17. C2×#17985113 | C22 | semidirect |
| 18. #22582815 | C22 | semidirect |
| 21. C2×Q16×C281 | C22 | semidirect |
| 24. M32×C281 | C22 | semidirect |
| 91. C281 | #2194 | semidirect |
| 94. #510 | D281 | semidirect |
| 106. C2×Q16 | C2×D281 | semidirect |
| 113. M32 | C2×D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31824265 | 2 |
| C2×#22582822 | 2 |
| #31823735 | 2 |
| #31823277 | 2 |
| #31823270 | 2 |
| #31823248 | 2 |
| #510×C281 | 2 |
| #2194 | 281 |