Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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. #31773906 | C2 | semidirect |
| 5. #31773658 | C2 | semidirect |
| 6. #31773656 | C2 | semidirect |
| 7. #419×C271 | C2 | semidirect |
| 11. #22576149 | C4 | semidirect |
| 42. C4×Dic271 | C2×C4 | semidirect |
| 48. C2×Q8×C271 | C2×C4 | semidirect |
| 107. C271 | #1885 | semidirect |
| 112. #419 | D271 | semidirect |
| 138. C2×Q8 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576149 | 2 |
| #31774371 | 2 |
| #31773906 | 2 |
| C2×#22576076 | 2 |
| #31773658 | 2 |
| #31773656 | 2 |
| #419×C271 | 2 |
| #1885 | 271 |