Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 8. #22576152 | C4 | direct (N × H) |
| 68. C4×C271 | #125 | semidirect |
| 76. C271 | C4×#125 | semidirect |
| 147. C4 | #22576152 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576152 | 2 |
| #31773795 | 2 |
| #31773781 | 2 |
| #31773763 | 2 |
| C4×Dic271⋊C4 | 2 |
| C4×C4⋊Dic271 | 2 |
| C43×C271 | 2 |
| C4×#125 | 271 |