Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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. #31774450 | C2 | semidirect |
| 5. #31773658 | C2 | semidirect |
| 6. #31773654 | C2 | semidirect |
| 7. #344×C271 | C2 | semidirect |
| 28. C2×Dic542 | Q8 | semidirect |
| 29. C2×D1084 | Q8 | semidirect |
| 102. C271 | #2031 | semidirect |
| 108. #344 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774450 | 2 |
| #31773913 | 2 |
| C2×#22576086 | 2 |
| #31773870 | 2 |
| #31773658 | 2 |
| #31773654 | 2 |
| #344×C271 | 2 |
| #2031 | 271 |