Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
258 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 47 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. #14545859 | C2 | semidirect |
| 2. (C2×#3633)⋊C8 | C2 | semidirect |
| 21. C2×Q16×C17 | C8 | semidirect |
| 25. C2×D136 | C8 | semidirect |
| 126. C2×Q16 | #3633 | semidirect |
| 145. C17 | #7114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545859 | 2 |
| (C2×#3633)⋊C8 | 2 |
| #14544935 | 2 |
| #7114 | 17 |