Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
866 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 312 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 |
|---|---|---|
| 2. #14544583 | C2 | semidirect |
| 5. #11763831 | C4 | semidirect |
| 146. C17 | #20539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763831 | 2 |
| #14544583 | 2 |
| #14544513 | 2 |
| #14531190 | 2 |
| #20539 | 17 |