Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
376 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 99 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×#22576091 | C2 | semidirect |
| 3. C2×#22576081 | C2 | semidirect |
| 4. C2×#22576080 | C2 | semidirect |
| 5. C2×#22576071 | C2 | semidirect |
| 6. #31773799 | C2 | semidirect |
| 7. #390×C271 | C2 | semidirect |
| 11. C2×#16864639 | C4 | semidirect |
| 69. C271⋊C8 | C22⋊C4 | semidirect |
| 120. C271 | #1972 | semidirect |
| 128. #390 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864639 | 2 |
| C2×#22576091 | 2 |
| C2×#22576081 | 2 |
| C2×#22576080 | 2 |
| C2×#22576071 | 2 |
| #31773799 | 2 |
| #390×C271 | 2 |
| #1972 | 271 |