Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31774445 | C2 | semidirect |
| 2. C4×#16864653 | C2 | semidirect |
| 3. #31774220 | C2 | semidirect |
| 4. #31774183 | C2 | semidirect |
| 5. #31774177 | C2 | semidirect |
| 6. #31774094 | C2 | semidirect |
| 7. #31774039 | C2 | semidirect |
| 8. #31774009 | C2 | semidirect |
| 9. #31773994 | C2 | semidirect |
| 10. #31773953 | C2 | semidirect |
| 11. #459×C271 | C2 | semidirect |
| 86. Dic542 | #41 | semidirect |
| 110. D4×C271 | #41 | semidirect |
| 144. C271 | #3115 | semidirect |
| 152. #459 | D271 | semidirect |
| 241. D4 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774445 | 2 |
| C4×#16864653 | 2 |
| #31774220 | 2 |
| #31774183 | 2 |
| #31774177 | 2 |
| #31774094 | 2 |
| #31774039 | 2 |
| #31774009 | 2 |
| #31773994 | 2 |
| #31773953 | 2 |
| #459×C271 | 2 |
| #3115 | 271 |