Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
542 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 78 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. #14545295 | C2 | semidirect |
| 3. #14544692 | C2 | semidirect |
| 5. #14543684 | C2 | semidirect |
| 6. #14543664 | C2 | semidirect |
| 28. #11762852 | C4 | semidirect |
| 29. #11762851 | C4 | semidirect |
| 30. #11762814 | C4 | semidirect |
| 32. C17×#418 | C4 | semidirect |
| 246. #418 | #595 | semidirect |
| 319. C17 | #9366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545295 | 2 |
| #14544923 | 2 |
| #14544692 | 2 |
| #14544180 | 2 |
| #14543684 | 2 |
| #14543664 | 2 |
| #14538722 | 2 |
| #9366 | 17 |