Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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. #31823514 | C2 | semidirect |
| 3. #31823485 | C2 | semidirect |
| 4. Q8⋊#14555886 | C2 | semidirect |
| 5. #31823192 | C2 | semidirect |
| 6. #31823190 | C2 | semidirect |
| 7. Q8⋊C8×C281 | C2 | semidirect |
| 105. C281 | #1495 | semidirect |
| 111. Q8⋊C8 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31824000 | 2 |
| #31823514 | 2 |
| #31823485 | 2 |
| Q8⋊#14555886 | 2 |
| #31823192 | 2 |
| #31823190 | 2 |
| Q8⋊C8×C281 | 2 |
| #1495 | 281 |