Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#22576149 | C2 | semidirect |
| 3. C2×#22576136 | C2 | semidirect |
| 4. #31773814 | C2 | semidirect |
| 5. #31773804 | C2 | semidirect |
| 6. #31773799 | C2 | semidirect |
| 7. #31773768 | C2 | semidirect |
| 8. C4×(C2×D271)⋊C4 | C2 | semidirect |
| 9. C2×C4⋊Q8×C271 | C2 | semidirect |
| 106. C2×C4×C271 | #41 | semidirect |
| 136. C271 | #2432 | semidirect |
| 139. C2×C4⋊Q8 | D271 | semidirect |
| 243. C2×C4 | #16864655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864655 | 2 |
| C2×#22576149 | 2 |
| C2×#22576136 | 2 |
| #31773814 | 2 |
| #31773804 | 2 |
| #31773799 | 2 |
| #31773768 | 2 |
| C4×(C2×D271)⋊C4 | 2 |
| C2×C4⋊Q8×C271 | 2 |
| #2432 | 271 |