Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
974 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 974 conjugacy classes of subgroups — too many to draw. Only its 226 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. #14545686 | C2 | semidirect |
| 2. #14545224 | C2 | semidirect |
| 4. #14544178 | C2 | semidirect |
| 5. #14544168 | C2 | semidirect |
| 21. #11763538 | C4 | semidirect |
| 22. #11763533 | C4 | semidirect |
| 25. Q8×D68 | C4 | semidirect |
| 31. C17×#557 | C4 | semidirect |
| 181. #557 | #595 | semidirect |
| 257. C17 | #17549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545686 | 2 |
| #14545224 | 2 |
| #14544188 | 2 |
| #14544178 | 2 |
| #14544168 | 2 |
| #14544157 | 2 |
| #14542881 | 2 |
| #17549 | 17 |