Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 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. #31774632 | C2 | semidirect |
| 2. D4×Dic542 | C2 | semidirect |
| 3. #31774258 | C2 | semidirect |
| 4. #31774244 | C2 | semidirect |
| 5. #31774186 | C2 | semidirect |
| 6. #31774182 | C2 | semidirect |
| 7. #31774114 | C2 | semidirect |
| 9. #31774027 | C2 | semidirect |
| 10. #31774006 | C2 | semidirect |
| 11. C4×SD16×C271 | C2 | semidirect |
| 124. C271 | #3373 | semidirect |
| 136. C4×SD16 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774632 | 2 |
| D4×Dic542 | 2 |
| #31774258 | 2 |
| #31774244 | 2 |
| #31774186 | 2 |
| #31774182 | 2 |
| #31774114 | 2 |
| #31774092 | 2 |
| #31774027 | 2 |
| #31774006 | 2 |
| C4×SD16×C271 | 2 |
| #3373 | 271 |