Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 2. #31773951 | C2 | direct (N × H) |
| 3. C2×Dic271⋊C8 | C2 | semidirect |
| 5. C2×#22576070 | C2 | semidirect |
| 16. Dic271⋊C8 | C22 | semidirect |
| 18. #22576070 | C22 | semidirect |
| 86. C2×C271 | #432 | semidirect |
| 90. C271 | C2×#432 | semidirect |
| 177. C2 | #31773951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic271 | 2 |
| #31773951 | 2 |
| C2×Dic271⋊C8 | 2 |
| C2×C22⋊(C271⋊C8) | 2 |
| C2×#22576070 | 2 |
| C2×C22⋊C8×C271 | 2 |
| C2×#432 | 271 |