Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. Q8×D1084 | C2 | semidirect |
| 2. #31774243 | C2 | semidirect |
| 3. #31774177 | C2 | semidirect |
| 4. #31774089 | C2 | semidirect |
| 5. Q8×C271⋊C8 | C2 | semidirect |
| 6. C4×#16864639 | C2 | semidirect |
| 7. #550×C271 | C2 | semidirect |
| 47. D1084 | #41 | semidirect |
| 53. Q8×C271 | D8 | semidirect |
| 81. C271 | #3358 | semidirect |
| 83. #550 | D271 | semidirect |
| 129. Q8 | #16864639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1084 | 2 |
| #31774243 | 2 |
| #31774177 | 2 |
| #31774089 | 2 |
| Q8×C271⋊C8 | 2 |
| C4×#16864639 | 2 |
| #550×C271 | 2 |
| #3358 | 271 |