Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×C4×Dic542 | C2 | semidirect |
| 2. #31774230 | C2 | semidirect |
| 4. #31774201 | C2 | semidirect |
| 5. #31774116 | C2 | semidirect |
| 6. #31774052 | C2 | semidirect |
| 8. #31774002 | C2 | semidirect |
| 9. #31773997 | C2 | semidirect |
| 10. #31773954 | C2 | semidirect |
| 131. C271 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic542 | 2 |
| #31774230 | 2 |
| #31774213 | 2 |
| #31774201 | 2 |
| #31774116 | 2 |
| #31774052 | 2 |
| #31774035 | 2 |
| #31774002 | 2 |
| #31773997 | 2 |
| #31773954 | 2 |
| #529×C271 | 2 |
| #3117 | 271 |