Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
224 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31773619 | C2 | semidirect |
| 4. C8×C271⋊C8 | C2 | semidirect |
| 17. #16864638 | C8 | semidirect |
| 31. C271⋊C8 | C2×C8 | semidirect |
| 32. C271⋊C8 | M16 | semidirect |
| 58. C271 | C8×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864638 | 2 |
| C2×C4×C271⋊C8 | 2 |
| #31773619 | 2 |
| C8×C271⋊C8 | 2 |
| #431×C271 | 2 |
| C8×M16 | 271 |