Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. #31823503 | C2 | semidirect |
| 5. #31823224 | C2 | semidirect |
| 6. #31823222 | C2 | semidirect |
| 7. #428×C281 | C2 | semidirect |
| 20. #22582795 | C4 | semidirect |
| 37. #17985122 | C2×C4 | semidirect |
| 51. M16×C281 | C2×C4 | semidirect |
| 114. C281 | #1856 | semidirect |
| 118. #428 | D281 | semidirect |
| 156. M16 | C4×D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31823937 | 2 |
| #31823503 | 2 |
| C2×#22582795 | 2 |
| #31823364 | 2 |
| #31823224 | 2 |
| #31823222 | 2 |
| #428×C281 | 2 |
| #1856 | 281 |