Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1148 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 224 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. #14545630 | C2 | semidirect |
| 2. #14544272 | C2 | semidirect |
| 3. #14544245 | C2 | semidirect |
| 4. #14544238 | C2 | semidirect |
| 8. #11763830 | C22 | semidirect |
| 9. C4×#63247 | C22 | semidirect |
| 10. #11763665 | C22 | semidirect |
| 11. #11763665 | C22 | semidirect |
| 12. #11763664 | C22 | semidirect |
| 13. #11763664 | C22 | semidirect |
| 200. C17 | #17688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545630 | 2 |
| #14544272 | 2 |
| #14544245 | 2 |
| #14544238 | 2 |
| #14542578 | 2 |
| #17688 | 17 |