Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
356 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 153 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. #31774301 | C2 | semidirect |
| 3. #31774298 | C2 | semidirect |
| 4. #31774297 | C2 | semidirect |
| 5. #31774294 | C2 | semidirect |
| 31. C2×C271⋊C8 | Q8 | semidirect |
| 44. C2×C8×C271 | Q8 | semidirect |
| 78. C271 | #3160 | semidirect |
| 114. C2×C8 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774450 | 2 |
| #31774301 | 2 |
| #31774298 | 2 |
| #31774297 | 2 |
| #31774294 | 2 |
| #31773935 | 2 |
| #31773933 | 2 |
| C2×C8×Dic271 | 2 |
| #427×C271 | 2 |
| #3160 | 271 |