Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
810 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 176 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. #14545513 | C2 | semidirect |
| 2. #14545511 | C2 | semidirect |
| 3. #14544922 | C2 | semidirect |
| 4. #14544920 | C2 | semidirect |
| 5. #14544776 | C2 | semidirect |
| 6. #14544773 | C2 | semidirect |
| 7. #14544709 | C2 | semidirect |
| 8. #14544502 | C2 | semidirect |
| 28. #11763190 | C4 | semidirect |
| 29. #11763188 | C4 | semidirect |
| 30. #11763185 | C4 | semidirect |
| 31. #11763182 | C4 | semidirect |
| 33. C17×#492 | C4 | semidirect |
| 188. #492 | #595 | semidirect |
| 250. C17 | #22282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545513 | 2 |
| #14545511 | 2 |
| #14544922 | 2 |
| #14544920 | 2 |
| #14544776 | 2 |
| #14544773 | 2 |
| #14544709 | 2 |
| #14544502 | 2 |
| #14539207 | 2 |
| #22282 | 17 |