Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31774607 | C2 | semidirect |
| 2. #31774251 | C2 | semidirect |
| 3. #31774247 | C2 | semidirect |
| 4. #31774204 | C2 | semidirect |
| 5. #31774187 | C2 | semidirect |
| 7. #31774099 | C2 | semidirect |
| 8. Q8×C271⋊C8 | C2 | semidirect |
| 9. C4×#16864641 | C2 | semidirect |
| 11. #556×C271 | C2 | semidirect |
| 120. C271 | #3360 | semidirect |
| 122. #556 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774607 | 2 |
| #31774251 | 2 |
| #31774247 | 2 |
| #31774204 | 2 |
| #31774187 | 2 |
| #31774109 | 2 |
| #31774099 | 2 |
| Q8×C271⋊C8 | 2 |
| C4×#16864641 | 2 |
| C4×#16864639 | 2 |
| #556×C271 | 2 |
| #3360 | 271 |