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. #31774448 | C2 | semidirect |
| 2. C4×#16864653 | C2 | semidirect |
| 3. #31774224 | C2 | semidirect |
| 4. #31774179 | C2 | semidirect |
| 5. #31774098 | C2 | semidirect |
| 6. #31774092 | C2 | semidirect |
| 7. #31774043 | C2 | semidirect |
| 8. #31774006 | C2 | semidirect |
| 9. #31773996 | C2 | semidirect |
| 10. #31773953 | C2 | semidirect |
| 11. #474×C271 | C2 | semidirect |
| 86. Dic542 | #41 | semidirect |
| 109. D4×C271 | #41 | semidirect |
| 144. C271 | #3115 | semidirect |
| 150. #474 | D271 | semidirect |
| 241. D4 | #16864655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774448 | 2 |
| C4×#16864653 | 2 |
| #31774224 | 2 |
| #31774179 | 2 |
| #31774098 | 2 |
| #31774092 | 2 |
| #31774043 | 2 |
| #31774006 | 2 |
| #31773996 | 2 |
| #31773953 | 2 |
| #474×C271 | 2 |
| #3115 | 271 |