Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
494 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 108 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. #14545114 | C2 | semidirect |
| 3. #14544721 | C2 | semidirect |
| 4. #14543841 | C2 | semidirect |
| 15. C4×D136 | C4 | semidirect |
| 16. D8×Dic17 | C4 | semidirect |
| 17. #11762891 | C4 | semidirect |
| 23. C4×D8×C17 | C4 | semidirect |
| 191. C4×D8 | #595 | semidirect |
| 248. C17 | #12813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545114 | 2 |
| C2×#11763721 | 2 |
| #14544721 | 2 |
| #14543841 | 2 |
| C4×D8×D17 | 2 |
| #12813 | 17 |