Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22576191 | C2 | semidirect |
| 3. C22×#16864644 | C2 | semidirect |
| 4. #31774057 | C2 | semidirect |
| 5. #31774052 | C2 | semidirect |
| 6. #31773905 | C2 | semidirect |
| 7. #31773891 | C2 | semidirect |
| 8. #31773864 | C2 | semidirect |
| 9. #536×C271 | C2 | semidirect |
| 140. C271 | #3011 | semidirect |
| 145. #536 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576207 | 2 |
| C2×#22576191 | 2 |
| C22×#16864644 | 2 |
| #31774057 | 2 |
| #31774052 | 2 |
| #31773905 | 2 |
| #31773891 | 2 |
| #31773864 | 2 |
| #536×C271 | 2 |
| #3011 | 271 |