Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22576208 | C2 | semidirect |
| 2. #31774695 | C2 | semidirect |
| 3. #31774079 | C2 | semidirect |
| 4. #31774069 | C2 | semidirect |
| 5. #31773915 | C2 | semidirect |
| 6. C2×#22576079 | C2 | semidirect |
| 7. #536×C271 | C2 | semidirect |
| 15. #22576191 | C22 | semidirect |
| 17. #22576186 | C22 | semidirect |
| 21. #22576088 | C22 | semidirect |
| 22. #22576079 | C22 | semidirect |
| 25. C4⋊Q8×C271 | C22 | semidirect |
| 26. #124×C271 | C22 | semidirect |
| 123. C271 | #3020 | semidirect |
| 127. #536 | D271 | semidirect |
| 147. C4⋊Q8 | C2×D271 | semidirect |
| 148. #124 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576208 | 2 |
| #31774695 | 2 |
| #31774079 | 2 |
| #31774069 | 2 |
| #31773915 | 2 |
| C2×#22576079 | 2 |
| #536×C271 | 2 |
| #3020 | 271 |