Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×#22576087 | C2 | semidirect |
| 3. C2×#22576086 | C2 | semidirect |
| 4. #31773896 | C2 | semidirect |
| 5. #31773766 | C2 | semidirect |
| 6. #31773665 | C2 | semidirect |
| 7. #417×C271 | C2 | semidirect |
| 48. C4×Dic271 | D4 | semidirect |
| 128. C271 | #2039 | semidirect |
| 134. #417 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774475 | 2 |
| C2×#22576087 | 2 |
| C2×#22576086 | 2 |
| #31773896 | 2 |
| #31773766 | 2 |
| #31773665 | 2 |
| #417×C271 | 2 |
| #2039 | 271 |