Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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. #31774026 | C2 | semidirect |
| 3. #31774024 | C2 | semidirect |
| 33. C2×C271⋊C8 | Q8 | semidirect |
| 83. C271 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774450 | 2 |
| #31774026 | 2 |
| #31774024 | 2 |
| #31773923 | 2 |
| #31773920 | 2 |
| #31773855 | 2 |
| #31773853 | 2 |
| C2×#22576070 | 2 |
| #424×C271 | 2 |
| #2961 | 271 |