Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
568 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 3. #14543605 | C2 | semidirect |
| 4. #14543604 | C2 | semidirect |
| 246. C17 | #7667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544640 | 2 |
| C2×#11763675 | 2 |
| #14543605 | 2 |
| #14543604 | 2 |
| #14537132 | 2 |
| #7667 | 17 |