Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
656 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 285 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 |
|---|---|---|
| 3. #31773766 | C2 | semidirect |
| 4. #31773762 | C2 | semidirect |
| 6. C4×Dic271⋊C4 | C2 | semidirect |
| 13. C2×C4×Dic271 | C4 | semidirect |
| 60. C2×C4×C271 | C4⋊C4 | semidirect |
| 80. Dic271 | #117 | semidirect |
| 86. C271 | #2285 | semidirect |
| 147. C2×C4 | Dic271⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576119 | 2 |
| C22×C4×Dic271 | 2 |
| #31773766 | 2 |
| #31773762 | 2 |
| #31773755 | 2 |
| C4×Dic271⋊C4 | 2 |
| C2×#117×C271 | 2 |
| #2285 | 271 |