Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D1084 | C2 | semidirect |
| 3. #31774248 | C2 | semidirect |
| 4. #31774229 | C2 | semidirect |
| 5. #31774182 | C2 | semidirect |
| 6. #31774125 | C2 | semidirect |
| 7. #31774102 | C2 | semidirect |
| 8. #31774034 | C2 | semidirect |
| 9. C8×D1084 | C2 | semidirect |
| 10. #103×D271 | C2 | semidirect |
| 11. C4×SD16×C271 | C2 | semidirect |
| 82. D1084 | SD16 | semidirect |
| 94. Q8×C271 | #41 | semidirect |
| 128. C271 | #3298 | semidirect |
| 138. C4×SD16 | D271 | semidirect |
| 213. Q8 | #16864654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1084 | 2 |
| #31774552 | 2 |
| #31774248 | 2 |
| #31774229 | 2 |
| #31774182 | 2 |
| #31774125 | 2 |
| #31774102 | 2 |
| #31774034 | 2 |
| C8×D1084 | 2 |
| #103×D271 | 2 |
| C4×SD16×C271 | 2 |
| #3298 | 271 |