Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
462 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 82 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. #14545561 | C2 | semidirect |
| 2. C2×#11763723 | C2 | semidirect |
| 3. #14545091 | C2 | semidirect |
| 4. #14544941 | C2 | semidirect |
| 5. #14543865 | C2 | semidirect |
| 6. #14543840 | C2 | semidirect |
| 24. #11763252 | C4 | semidirect |
| 25. #11763249 | C4 | semidirect |
| 27. #11763245 | C4 | semidirect |
| 32. C17×#509 | C4 | semidirect |
| 224. #509 | #595 | semidirect |
| 302. C17 | #13021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545561 | 2 |
| C2×#11763723 | 2 |
| #14545091 | 2 |
| #14544941 | 2 |
| #14543865 | 2 |
| #14543840 | 2 |
| #14541916 | 2 |
| #13021 | 17 |