Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
190 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #14543950 | C2 | semidirect |
| 4. #14543949 | C2 | semidirect |
| 14. #11762643 | C4 | semidirect |
| 16. C32×D17 | C4 | semidirect |
| 17. C17×M64 | C4 | semidirect |
| 32. C17×C32 | C2×C4 | semidirect |
| 33. #10587465 | C2×C4 | semidirect |
| 87. M64 | #595 | semidirect |
| 97. D17 | #1426 | semidirect |
| 113. C32 | C2×#595 | semidirect |
| 114. C17 | C2×#1426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#368 | 2 |
| C2×#11763736 | 2 |
| #14543950 | 2 |
| #14543949 | 2 |
| D17×M64 | 2 |
| C2×#1426 | 17 |