Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
256 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 21. #103×C271 | C4 | semidirect |
| 105. C271 | #1933 | semidirect |
| 123. #103 | Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576084 | 2 |
| C2×C8×Dic271 | 2 |
| #31773804 | 2 |
| #31773796 | 2 |
| #31773660 | 2 |
| #31773659 | 2 |
| C2×#103×C271 | 2 |
| #1933 | 271 |