Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
878 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 106 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. #14545106 | C2 | semidirect |
| 2. #14545094 | C2 | semidirect |
| 3. #14545021 | C2 | semidirect |
| 4. #14544666 | C2 | semidirect |
| 20. C2×#10587605 | C4 | semidirect |
| 22. C2×#10587590 | C4 | semidirect |
| 23. C2×Q16×D17 | C4 | semidirect |
| 26. C22×Q16×C17 | C4 | semidirect |
| 235. C22×Q16 | #595 | semidirect |
| 305. C17 | #12742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545106 | 2 |
| #14545094 | 2 |
| #14545021 | 2 |
| #14544666 | 2 |
| C2×#11763622 | 2 |
| #12742 | 17 |