Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #31823195 | C2 | semidirect |
| 5. Q8⋊#14555886 | C2 | semidirect |
| 6. #31823193 | C2 | semidirect |
| 7. Q8⋊C8×C281 | C2 | semidirect |
| 60. Dic562 | M16 | semidirect |
| 76. Q8×C281 | M16 | semidirect |
| 104. C281 | #1491 | semidirect |
| 112. Q8⋊C8 | D281 | semidirect |
| 167. Q8 | #17985121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D281 | 2 |
| #31823519 | 2 |
| C4×#17985121 | 2 |
| #31823195 | 2 |
| Q8⋊#14555886 | 2 |
| #31823193 | 2 |
| Q8⋊C8×C281 | 2 |
| #1491 | 281 |