Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#22576191 | C2 | semidirect |
| 3. #31774276 | C2 | semidirect |
| 4. #31774153 | C2 | semidirect |
| 5. #31774107 | C2 | semidirect |
| 6. #31774099 | C2 | semidirect |
| 7. #31774057 | C2 | semidirect |
| 8. #31774053 | C2 | semidirect |
| 9. C4×#16864641 | C2 | semidirect |
| 10. #31773975 | C2 | semidirect |
| 11. D4×Q8×C271 | C2 | semidirect |
| 53. #16864641 | D4 | semidirect |
| 124. C4×C271 | #137 | semidirect |
| 134. C271 | #3276 | semidirect |
| 137. D4×Q8 | D271 | semidirect |
| 261. C4 | #22576191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576191 | 2 |
| #31774552 | 2 |
| #31774276 | 2 |
| #31774153 | 2 |
| #31774107 | 2 |
| #31774099 | 2 |
| #31774057 | 2 |
| #31774053 | 2 |
| C4×#16864641 | 2 |
| #31773975 | 2 |
| D4×Q8×C271 | 2 |
| #3276 | 271 |