Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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. #31823215 | C2 | semidirect |
| 5. #31823214 | C2 | semidirect |
| 6. #31823213 | C2 | semidirect |
| 7. #335×C281 | C2 | semidirect |
| 53. #14555886 | M16 | semidirect |
| 60. C8×C281 | M16 | semidirect |
| 77. C281 | #1569 | semidirect |
| 83. #335 | D281 | semidirect |
| 138. C8 | #17985121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31823519 | 2 |
| #31823485 | 2 |
| C4×#17985121 | 2 |
| #31823215 | 2 |
| #31823214 | 2 |
| #31823213 | 2 |
| #335×C281 | 2 |
| #1569 | 281 |