Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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×#22582813 | C2 | semidirect |
| 3. C2×#22582812 | C2 | semidirect |
| 6. #31823225 | C2 | semidirect |
| 7. #340×C281 | C2 | semidirect |
| 19. #22582791 | C4 | semidirect |
| 39. C2×#14555886 | C2×C4 | semidirect |
| 51. C2×C8×C281 | C2×C4 | semidirect |
| 105. C2×D281 | #107 | semidirect |
| 123. C281 | #1852 | semidirect |
| 131. #340 | D281 | semidirect |
| 169. C2×C8 | C4×D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D281 | 2 |
| C2×#22582813 | 2 |
| C2×#22582812 | 2 |
| C2×#22582791 | 2 |
| #31823320 | 2 |
| #31823225 | 2 |
| #340×C281 | 2 |
| #1852 | 281 |