Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774621 | C2 | semidirect |
| 3. #31774234 | C2 | semidirect |
| 4. #31774224 | C2 | semidirect |
| 5. #31774179 | C2 | semidirect |
| 6. #31774174 | C2 | semidirect |
| 7. #31774144 | C2 | semidirect |
| 8. C4×#16864643 | C2 | semidirect |
| 9. #31773976 | C2 | semidirect |
| 10. #31773938 | C2 | semidirect |
| 11. #500×C271 | C2 | semidirect |
| 99. C8×C271 | #41 | semidirect |
| 122. C271 | #3353 | semidirect |
| 126. #500 | D271 | semidirect |
| 222. C8 | #16864655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774621 | 2 |
| #31774550 | 2 |
| #31774234 | 2 |
| #31774224 | 2 |
| #31774179 | 2 |
| #31774174 | 2 |
| #31774144 | 2 |
| C4×#16864643 | 2 |
| #31773976 | 2 |
| #31773938 | 2 |
| #500×C271 | 2 |
| #3353 | 271 |