Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
138 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 67 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. C4⋊(C271⋊C16) | C2 | semidirect |
| 5. #31773672 | C2 | semidirect |
| 6. C16×Dic271 | C2 | semidirect |
| 7. C4⋊C16×C271 | C2 | semidirect |
| 66. C271 | #2164 | semidirect |
| 70. C4⋊C16 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31773851 | 2 |
| C4⋊(C271⋊C16) | 2 |
| (C2×D271)⋊C16 | 2 |
| #31773672 | 2 |
| C16×Dic271 | 2 |
| C4⋊C16×C271 | 2 |
| #2164 | 271 |