Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. D16×Dic17 | C2 | semidirect |
| 3. #14530630 | C2 | semidirect |
| 4. #14526985 | C2 | semidirect |
| 5. #14526963 | C2 | semidirect |
| 6. #14526917 | C2 | semidirect |
| 7. C17×#1415 | C2 | semidirect |
| 11. #11762644 | C4 | semidirect |
| 25. C17×D16 | C2×C4 | semidirect |
| 34. D272 | C2×C4 | semidirect |
| 36. #10587465 | C2×C4 | semidirect |
| 77. #1415 | D17 | semidirect |
| 116. D16 | C4×D17 | semidirect |
| 126. C17 | #13654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762644 | 2 |
| D16×Dic17 | 2 |
| #14530630 | 2 |
| #14526985 | 2 |
| #14526963 | 2 |
| #14526917 | 2 |
| C17×#1415 | 2 |
| #13654 | 17 |