Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
194 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 50 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. #14545187 | C2 | semidirect |
| 2. #14545182 | C2 | semidirect |
| 3. #14543950 | C2 | semidirect |
| 4. #14543939 | C2 | semidirect |
| 5. #14543938 | C2 | semidirect |
| 6. #14543893 | C2 | semidirect |
| 18. #11762646 | C4 | semidirect |
| 19. D544 | C4 | semidirect |
| 20. #11762644 | C4 | semidirect |
| 22. C17×SD64 | C4 | semidirect |
| 33. C17×Q32 | C2×C4 | semidirect |
| 38. D272 | C2×C4 | semidirect |
| 41. C17×C32 | C2×C4 | semidirect |
| 42. #10587465 | C2×C4 | semidirect |
| 103. SD64 | #595 | semidirect |
| 122. Q32 | C2×#595 | semidirect |
| 137. C32 | C2×#595 | semidirect |
| 138. C17 | #13658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545187 | 2 |
| #14545182 | 2 |
| #14543950 | 2 |
| #14543939 | 2 |
| #14543938 | 2 |
| #14543893 | 2 |
| #14531098 | 2 |
| #13658 | 17 |