Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
256 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 16. Dic271⋊C8 | C4 | semidirect |
| 91. Dic271 | #107 | semidirect |
| 99. C271 | #1947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576093 | 2 |
| C2×Dic271⋊C8 | 2 |
| #31773766 | 2 |
| C4⋊C4×Dic271 | 2 |
| #31773660 | 2 |
| #31773659 | 2 |
| C2×#107×C271 | 2 |
| #1947 | 271 |