Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #31774307 | C2 | semidirect |
| 4. #31774306 | C2 | semidirect |
| 5. #31774303 | C2 | semidirect |
| 6. #31774301 | C2 | semidirect |
| 7. #31774294 | C2 | semidirect |
| 11. #501×C271 | C2 | semidirect |
| 52. #16864637 | Q8 | semidirect |
| 95. C271⋊C8 | C2×Q8 | semidirect |
| 103. C8×C271 | C2×Q8 | semidirect |
| 124. C271 | #3165 | semidirect |
| 131. #501 | D271 | semidirect |
| 228. C8 | Q8×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774453 | 2 |
| C4⋊Q8×D271 | 2 |
| #31774307 | 2 |
| #31774306 | 2 |
| #31774303 | 2 |
| #31774301 | 2 |
| #31774294 | 2 |
| #31773938 | 2 |
| #31773936 | 2 |
| #31773849 | 2 |
| #501×C271 | 2 |
| #3165 | 271 |