Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. #31774247 | C2 | semidirect |
| 3. #31774225 | C2 | semidirect |
| 4. #31774182 | C2 | semidirect |
| 5. #31774128 | C2 | semidirect |
| 6. #31774099 | C2 | semidirect |
| 7. #31774036 | C2 | semidirect |
| 8. C4×#16864641 | C2 | semidirect |
| 9. D4×C271⋊C8 | C2 | semidirect |
| 10. C2×#22576084 | C2 | semidirect |
| 11. D4×Q8×C271 | C2 | semidirect |
| 94. Q8×C271 | #41 | semidirect |
| 95. D4×C271 | SD16 | semidirect |
| 128. C271 | #3298 | semidirect |
| 130. D4×Q8 | D271 | semidirect |
| 213. Q8 | #16864653 | semidirect |
| 217. D4 | #16864641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774551 | 2 |
| #31774247 | 2 |
| #31774225 | 2 |
| #31774182 | 2 |
| #31774128 | 2 |
| #31774099 | 2 |
| #31774036 | 2 |
| C4×#16864641 | 2 |
| D4×C271⋊C8 | 2 |
| C2×#22576084 | 2 |
| D4×Q8×C271 | 2 |
| #3298 | 271 |