Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22576182 | C2 | semidirect |
| 2. #31774408 | C2 | semidirect |
| 3. #31774155 | C2 | semidirect |
| 4. #31774150 | C2 | semidirect |
| 5. #31774143 | C2 | semidirect |
| 6. #31773935 | C2 | semidirect |
| 7. #31773894 | C2 | semidirect |
| 8. C22×M16×C271 | C2 | semidirect |
| 11. C2×Dic1084 | C22 | semidirect |
| 12. C2×#16864643 | C22 | semidirect |
| 13. C2×D2168 | C22 | semidirect |
| 20. #22576094 | C22 | semidirect |
| 21. #22576092 | C22 | semidirect |
| 22. #22576085 | C22 | semidirect |
| 23. #22576082 | C22 | semidirect |
| 56. C2×C8×C271 | D4 | semidirect |
| 105. C271 | #3054 | semidirect |
| 108. C22×M16 | D271 | semidirect |
| 156. C2×C8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576182 | 2 |
| #31774408 | 2 |
| #31774155 | 2 |
| #31774150 | 2 |
| #31774143 | 2 |
| #31773935 | 2 |
| #31773894 | 2 |
| C22×M16×C271 | 2 |
| #3054 | 271 |