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×#16864655 | C2 | semidirect |
| 3. #31774223 | C2 | semidirect |
| 4. #31774174 | C2 | semidirect |
| 5. #31774097 | C2 | semidirect |
| 6. #31774093 | C2 | semidirect |
| 7. #31774045 | C2 | semidirect |
| 8. #31774008 | C2 | semidirect |
| 9. #31774000 | C2 | semidirect |
| 10. #31773953 | C2 | semidirect |
| 11. #475×C271 | C2 | semidirect |
| 93. D1084 | #41 | semidirect |
| 109. Q8×C271 | #41 | semidirect |
| 144. C271 | #3115 | semidirect |
| 149. #475 | D271 | semidirect |
| 233. Q8 | #16864655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774448 | 2 |
| C4×#16864655 | 2 |
| #31774223 | 2 |
| #31774174 | 2 |
| #31774097 | 2 |
| #31774093 | 2 |
| #31774045 | 2 |
| #31774008 | 2 |
| #31774000 | 2 |
| #31773953 | 2 |
| #475×C271 | 2 |
| #3115 | 271 |