Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
384 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. #31774193 | C2 | semidirect |
| 5. #31774192 | C2 | semidirect |
| 6. #31774104 | C2 | semidirect |
| 8. Q16×Dic271 | C2 | semidirect |
| 9. #31773989 | C2 | semidirect |
| 11. #462×C271 | C2 | semidirect |
| 98. C4×D271 | Q16 | semidirect |
| 132. C271 | #3104 | semidirect |
| 140. #462 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| C4×Q8×D271 | 2 |
| #31774231 | 2 |
| #31774193 | 2 |
| #31774192 | 2 |
| #31774104 | 2 |
| #31774051 | 2 |
| Q16×Dic271 | 2 |
| #31773989 | 2 |
| #31773949 | 2 |
| #462×C271 | 2 |
| #3104 | 271 |