Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
202 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 56 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. Q32×#595 | C2 | semidirect |
| 3. #14543946 | C2 | semidirect |
| 4. #14543934 | C2 | semidirect |
| 6. C32×#595 | C2 | semidirect |
| 18. #11762648 | C4 | semidirect |
| 19. #11762647 | C4 | semidirect |
| 20. #11762646 | C4 | semidirect |
| 22. C17×SD64 | C4 | semidirect |
| 33. C17×Q32 | C2×C4 | semidirect |
| 37. Dic136 | C2×C4 | semidirect |
| 41. C17×C32 | C2×C4 | semidirect |
| 42. #10587465 | C2×C4 | semidirect |
| 96. #595 | SD64 | direct (N × H) |
| 108. SD64 | #595 | direct (N × H) |
| 127. Q32 | C2×#595 | semidirect |
| 140. C32 | C2×#595 | semidirect |
| 141. C17 | C4×SD64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×#595 | 2 |
| D16×#595 | 2 |
| #14543946 | 2 |
| #14543934 | 2 |
| #14543933 | 2 |
| C32×#595 | 2 |
| D17×SD64 | 2 |
| C4×SD64 | 17 |