Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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. #31823904 | C2 | semidirect |
| 3. C2×#22582822 | C2 | semidirect |
| 4. #31823275 | C2 | semidirect |
| 5. #31823269 | C2 | semidirect |
| 6. #31823247 | C2 | semidirect |
| 7. #473×C281 | C2 | semidirect |
| 18. #22582819 | C22 | semidirect |
| 19. C2×#17985113 | C22 | semidirect |
| 21. C2×Q16×C281 | C22 | semidirect |
| 23. #108×C281 | C22 | semidirect |
| 91. C281 | #2194 | semidirect |
| 96. #473 | D281 | semidirect |
| 106. C2×Q16 | C2×D281 | semidirect |
| 115. #108 | C2×D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31824268 | 2 |
| #31823904 | 2 |
| C2×#22582822 | 2 |
| #31823275 | 2 |
| #31823269 | 2 |
| #31823247 | 2 |
| #473×C281 | 2 |
| #2194 | 281 |