Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
492 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14545279 | C2 | semidirect |
| 3. #14544298 | C2 | semidirect |
| 5. #14543638 | C2 | semidirect |
| 6. #14543607 | C2 | semidirect |
| 22. #11763181 | C4 | semidirect |
| 23. #11763160 | C4 | semidirect |
| 24. #11763159 | C4 | semidirect |
| 28. C17×#492 | C4 | semidirect |
| 103. C4×#595 | SD16 | semidirect |
| 202. #492 | #595 | semidirect |
| 270. C17 | #9301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545279 | 2 |
| #14544922 | 2 |
| #14544298 | 2 |
| #14544213 | 2 |
| #14543638 | 2 |
| #14543607 | 2 |
| #14539705 | 2 |
| #9301 | 17 |