Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22576183 | C2 | semidirect |
| 2. #31774566 | C2 | semidirect |
| 3. #31774272 | C2 | semidirect |
| 4. #31774133 | C2 | semidirect |
| 5. #31774130 | C2 | semidirect |
| 6. #31774095 | C2 | semidirect |
| 7. #31774042 | C2 | semidirect |
| 8. #31774041 | C2 | semidirect |
| 9. Q16×Dic271 | C2 | semidirect |
| 10. C8×C22⋊D271 | C2 | semidirect |
| 11. C2×#135×C271 | C2 | semidirect |
| 74. Q16×C271 | D4 | semidirect |
| 134. Dic271 | #135 | semidirect |
| 142. C271 | #3287 | semidirect |
| 145. C2×#135 | D271 | semidirect |
| 202. Q16 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576183 | 2 |
| #31774566 | 2 |
| #31774272 | 2 |
| #31774133 | 2 |
| #31774130 | 2 |
| #31774095 | 2 |
| #31774042 | 2 |
| #31774041 | 2 |
| Q16×Dic271 | 2 |
| C8×C22⋊D271 | 2 |
| C2×#135×C271 | 2 |
| #3287 | 271 |