Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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×Dic542 | C2 | semidirect |
| 4. #31774248 | C2 | semidirect |
| 6. #31774181 | C2 | semidirect |
| 8. #31774107 | C2 | semidirect |
| 9. #31774027 | C2 | semidirect |
| 10. #31774001 | C2 | semidirect |
| 116. C271 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic542 | 2 |
| #31774617 | 2 |
| #31774255 | 2 |
| #31774248 | 2 |
| #31774187 | 2 |
| #31774181 | 2 |
| #31774117 | 2 |
| #31774107 | 2 |
| #31774027 | 2 |
| #31774001 | 2 |
| C4×SD16×C271 | 2 |
| #3369 | 271 |