Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
890 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 140 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. #14545028 | C2 | semidirect |
| 2. C2×#11763708 | C2 | semidirect |
| 3. #14545020 | C2 | semidirect |
| 4. #14545014 | C2 | semidirect |
| 6. C2×#10587538 | C22 | semidirect |
| 7. C2×#10587538 | C22 | semidirect |
| 8. C22×#63216 | C22 | semidirect |
| 226. C17 | #12685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545028 | 2 |
| C2×#11763708 | 2 |
| #14545020 | 2 |
| #14545014 | 2 |
| #14543497 | 2 |
| #12685 | 17 |