Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
416 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 416 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. #14545012 | C2 | semidirect |
| 2. #14544661 | C2 | semidirect |
| 3. #14543772 | C2 | semidirect |
| 4. #14543770 | C2 | semidirect |
| 14. #11763047 | C4 | semidirect |
| 16. #11763042 | C4 | semidirect |
| 20. #11762847 | C4 | semidirect |
| 22. C2×C17×#135 | C4 | semidirect |
| 174. C2×#135 | #595 | semidirect |
| 234. C17 | #11890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545012 | 2 |
| #14544661 | 2 |
| #14543772 | 2 |
| #14543770 | 2 |
| #14538361 | 2 |
| #11890 | 17 |