Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
450 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 114 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. #14544990 | C2 | semidirect |
| 2. #14544331 | C2 | semidirect |
| 3. #14543743 | C2 | semidirect |
| 7. #11763698 | C22 | semidirect |
| 10. #11763670 | C22 | semidirect |
| 29. C2×D136 | C8 | semidirect |
| 177. C17 | #11599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544990 | 2 |
| #14544331 | 2 |
| #14543743 | 2 |
| C2×#11762891 | 2 |
| #11599 | 17 |