Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 179 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. #14540162 | C2 | semidirect |
| 2. #14539210 | C2 | semidirect |
| 3. #14527929 | C2 | semidirect |
| 4. #14527900 | C2 | semidirect |
| 5. #14527867 | C2 | semidirect |
| 6. #14527838 | C2 | semidirect |
| 7. #14527519 | C2 | semidirect |
| 8. #14527235 | C2 | semidirect |
| 9. C17×#3549 | C2 | semidirect |
| 11. #11763359 | C22 | semidirect |
| 13. #11763188 | C22 | semidirect |
| 15. #11763183 | C22 | semidirect |
| 17. #11763099 | C22 | semidirect |
| 20. #11763004 | C22 | semidirect |
| 22. #11762833 | C22 | semidirect |
| 23. C2×C4×#3622 | C22 | semidirect |
| 24. #11762558 | C22 | semidirect |
| 26. D4⋊#3622 | C22 | semidirect |
| 27. D4⋊#3622 | C22 | semidirect |
| 181. #3549 | D17 | semidirect |
| 292. C17 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14540162 | 2 |
| #14539210 | 2 |
| #14527929 | 2 |
| #14527900 | 2 |
| #14527867 | 2 |
| #14527838 | 2 |
| #14527519 | 2 |
| #14527235 | 2 |
| C17×#3549 | 2 |
| #18686 | 17 |