Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
| 4. #31773644 | C2 | semidirect |
| 5. Q8⋊(C271⋊C8) | C2 | semidirect |
| 6. #31773624 | C2 | semidirect |
| 7. #460×C271 | C2 | semidirect |
| 56. D1084 | SD16 | semidirect |
| 66. Q8×C271 | D8 | semidirect |
| 99. C271 | #1627 | semidirect |
| 103. #460 | D271 | semidirect |
| 157. 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 |
| #31774089 | 2 |
| #31773644 | 2 |
| Q8⋊(C271⋊C8) | 2 |
| #31773624 | 2 |
| #460×C271 | 2 |
| #1627 | 271 |