Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
994 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 166 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. #14544445 | C2 | semidirect |
| 2. #14543601 | C2 | semidirect |
| 3. #14543600 | C2 | semidirect |
| 7. #11763675 | C22 | semidirect |
| 23. C2×D4×D17 | C8 | semidirect |
| 57. C2×D4×C17 | C2×C8 | semidirect |
| 72. C2×D68 | C2×C8 | semidirect |
| 202. D17 | #1270 | semidirect |
| 232. C17 | C2×#1270 | semidirect |
| 253. C2×D4 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544445 | 2 |
| #14543601 | 2 |
| #14543600 | 2 |
| D17×#390 | 2 |
| C2×#1270 | 17 |