Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 2. #31774380 | C2 | semidirect |
| 3. #31773907 | C2 | semidirect |
| 4. #31773899 | C2 | semidirect |
| 5. #31773894 | C2 | semidirect |
| 6. C2×#22576085 | C2 | semidirect |
| 7. C2×#131×C271 | C2 | semidirect |
| 9. #22576207 | C4 | semidirect |
| 28. #16864654 | C2×C4 | semidirect |
| 32. C2×Dic542 | C2×C4 | semidirect |
| 94. C271 | #2898 | semidirect |
| 97. C2×#131 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576207 | 2 |
| #31774380 | 2 |
| #31773907 | 2 |
| #31773899 | 2 |
| #31773894 | 2 |
| C2×#22576085 | 2 |
| C2×#131×C271 | 2 |
| #2898 | 271 |