Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
680 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 25. C22×Q8×C17 | C8 | semidirect |
| 34. C22×Dic34 | C8 | semidirect |
| 35. C22×Dic34 | C8 | semidirect |
| 46. C22⋊#3633 | Q8 | semidirect |
| 232. C22×Q8 | #3633 | semidirect |
| 257. C17 | #9878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545924 | 2 |
| C4×C22⋊#3633 | 2 |
| #14545793 | 2 |
| C2×(C2×#595)⋊Q8 | 2 |
| #9878 | 17 |