Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 4. #31774193 | C2 | semidirect |
| 5. #31774108 | C2 | semidirect |
| 7. C4×Dic1084 | C2 | semidirect |
| 77. C2×C4×C271 | Q16 | semidirect |
| 103. C271 | #3104 | semidirect |
| 181. C2×C4 | Dic1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| C2×C4×Dic542 | 2 |
| #31774233 | 2 |
| #31774193 | 2 |
| #31774108 | 2 |
| #31774055 | 2 |
| C4×Dic1084 | 2 |
| #431×C271 | 2 |
| #3104 | 271 |