Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
234 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 60 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. #14544434 | C2 | semidirect |
| 2. #14544382 | C2 | semidirect |
| 3. #14543809 | C2 | semidirect |
| 4. #14543743 | C2 | semidirect |
| 5. #14543742 | C2 | semidirect |
| 6. #14543703 | C2 | semidirect |
| 64. D136 | M16 | semidirect |
| 152. C17 | #12078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544434 | 2 |
| #14544382 | 2 |
| #14543809 | 2 |
| #14543743 | 2 |
| #14543742 | 2 |
| #14543703 | 2 |
| #14530657 | 2 |
| #12078 | 17 |