Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 336 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. #14545148 | C2 | semidirect |
| 2. #14544705 | C2 | semidirect |
| 3. #14543772 | C2 | semidirect |
| 13. #11763210 | C4 | semidirect |
| 14. #11763194 | C4 | semidirect |
| 20. C4×D136 | C4 | semidirect |
| 22. C4×Q16×C17 | C4 | semidirect |
| 154. C4×Q16 | #595 | semidirect |
| 201. C17 | #11860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545148 | 2 |
| #14544705 | 2 |
| #14543772 | 2 |
| #14543771 | 2 |
| #14539357 | 2 |
| #11860 | 17 |