Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. #31823836 | C2 | semidirect |
| 2. #31823743 | C2 | semidirect |
| 4. #31823214 | C2 | semidirect |
| 5. #31823210 | C2 | semidirect |
| 6. #31823206 | C2 | semidirect |
| 7. C8×D4×C281 | C2 | semidirect |
| 56. D4×C281 | SD16 | semidirect |
| 65. C8×C281 | D8 | semidirect |
| 85. C281 | #1665 | semidirect |
| 90. C8×D4 | D281 | semidirect |
| 139. D4 | #17985127 | semidirect |
| 151. C8 | #17985123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31823836 | 2 |
| #31823743 | 2 |
| #31823658 | 2 |
| #31823214 | 2 |
| #31823210 | 2 |
| #31823206 | 2 |
| C8×D4×C281 | 2 |
| #1665 | 281 |