Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×Q16×D271 | C2 | semidirect |
| 4. #31774276 | C2 | semidirect |
| 5. #31774137 | C2 | semidirect |
| 6. #31774108 | C2 | semidirect |
| 7. #31774054 | C2 | semidirect |
| 8. #31774051 | C2 | semidirect |
| 9. C4×#16864644 | C2 | semidirect |
| 11. #462×C271 | C2 | semidirect |
| 57. #16864644 | D4 | semidirect |
| 89. D1084 | Q16 | semidirect |
| 114. C2×D271 | C2×Q16 | semidirect |
| 119. C4×C271 | C2×Q16 | semidirect |
| 130. C271 | D4×Q16 | semidirect |
| 138. #462 | D271 | semidirect |
| 254. C4 | Q16×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D271 | 2 |
| Q8×D1084 | 2 |
| #31774562 | 2 |
| #31774276 | 2 |
| #31774137 | 2 |
| #31774108 | 2 |
| #31774054 | 2 |
| #31774051 | 2 |
| C4×#16864644 | 2 |
| #31773962 | 2 |
| #462×C271 | 2 |
| D4×Q16 | 271 |