Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
544 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 92 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. #14544976 | C2 | semidirect |
| 3. #14544297 | C2 | semidirect |
| 5. #14543654 | C2 | semidirect |
| 6. #14543629 | C2 | semidirect |
| 120. #63247 | SD16 | semidirect |
| 323. C17 | #9247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545524 | 2 |
| #14544976 | 2 |
| #14544297 | 2 |
| #14544111 | 2 |
| #14543654 | 2 |
| #14543629 | 2 |
| C2×#11763013 | 2 |
| #9247 | 17 |