Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
546 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 124 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. #14545677 | C2 | semidirect |
| 3. #14544027 | C2 | semidirect |
| 4. #14543608 | C2 | semidirect |
| 25. C17×#124 | C8 | semidirect |
| 174. #124 | #3624 | semidirect |
| 201. C17 | #9102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545677 | 2 |
| #14544083 | 2 |
| #14544027 | 2 |
| #14543608 | 2 |
| #14531497 | 2 |
| #9102 | 17 |