Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
606 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 120 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. #14544674 | C2 | semidirect |
| 2. C4×C22⋊#3624 | C2 | semidirect |
| 3. #14543602 | C2 | semidirect |
| 4. #14543600 | C2 | semidirect |
| 32. C17×#121 | C8 | semidirect |
| 233. #121 | #3624 | semidirect |
| 257. C17 | #7582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544674 | 2 |
| C4×C22⋊#3624 | 2 |
| #14543602 | 2 |
| #14543600 | 2 |
| #121×Dic17 | 2 |
| #7582 | 17 |