Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
342 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 131 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. C22×#10587465 | C2 | semidirect |
| 2. C2×#11762635 | C2 | semidirect |
| 3. #14526962 | C2 | direct (N × H) |
| 7. C2×#10587465 | C22 | semidirect |
| 9. #11762635 | C22 | semidirect |
| 13. C2×C17×D16 | C4 | semidirect |
| 25. C17×D16 | C2×C4 | semidirect |
| 89. C2×D16 | Dic17 | semidirect |
| 98. C2×C17 | #1415 | semidirect |
| 111. D16 | C2×Dic17 | semidirect |
| 119. C17 | C2×#1415 | semidirect |
| 169. C2 | #14526962 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587465 | 2 |
| C2×#11762635 | 2 |
| #14526962 | 2 |
| C22×C17×D16 | 2 |
| C2×#1415 | 17 |