Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #31773795 | C2 | semidirect |
| 4. #31773786 | C2 | semidirect |
| 5. #31773759 | C2 | semidirect |
| 6. #31773756 | C2 | semidirect |
| 7. C4×C4⋊Dic271 | C2 | semidirect |
| 8. #376×C271 | C2 | semidirect |
| 11. C4×D1084 | C4 | semidirect |
| 96. C271 | #2319 | semidirect |
| 105. #376 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1084 | 2 |
| #31773799 | 2 |
| #31773795 | 2 |
| #31773786 | 2 |
| #31773759 | 2 |
| #31773756 | 2 |
| C4×C4⋊Dic271 | 2 |
| #376×C271 | 2 |
| #2319 | 271 |