Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
292 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 12. C4⋊Q8×C271 | C4 | semidirect |
| 20. C4⋊Dic271 | Q8 | semidirect |
| 69. C271 | #1988 | semidirect |
| 78. C4⋊Q8 | Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C271⋊C8) | 2 |
| C4×C4⋊Dic271 | 2 |
| #31773659 | 2 |
| C2×C4⋊Q8×C271 | 2 |
| #1988 | 271 |