Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3798 conjugacy classes of subgroups; only the 824 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 824 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. #14545328 | C2 | direct (N × H) |
| 2. C2×#11763757 | C2 | semidirect |
| 3. C2×#11763754 | C2 | semidirect |
| 7. #11763757 | C22 | semidirect |
| 8. #11763754 | C22 | semidirect |
| 11. C2×#10587560 | C4 | semidirect |
| 12. C2×#10587626 | C4 | semidirect |
| 13. #127×D17 | C4 | semidirect |
| 16. C2×C17×#127 | C4 | semidirect |
| 21. C22×D4×C17 | C2×C4 | semidirect |
| 22. C22×C22⋊D17 | C2×C4 | semidirect |
| 25. C2×D4×D17 | C2×C4 | semidirect |
| 27. C22×D68 | C2×C4 | semidirect |
| 31. C17×#127 | C2×C4 | semidirect |
| 32. C2×C42×C17 | C2×C4 | semidirect |
| 33. #10587626 | C2×C4 | semidirect |
| 34. C2×C4×Dic17 | C2×C4 | semidirect |
| 35. #10587560 | C2×C4 | semidirect |
| 36. C42×D17 | C2×C4 | semidirect |
| 51. C2×D4×C17 | C22×C4 | semidirect |
| 54. C2×C22⋊D17 | C22×C4 | semidirect |
| 60. C2×D68 | C22×C4 | semidirect |
| 65. C42×C17 | C22×C4 | semidirect |
| 66. C4×Dic17 | C22×C4 | semidirect |
| 118. C2×#127 | #595 | semidirect |
| 125. C2×C17 | #2380 | semidirect |
| 128. D17 | #2380 | semidirect |
| 137. C22×D4 | C2×#595 | semidirect |
| 144. #127 | C2×#595 | semidirect |
| 150. C2×C42 | C2×#595 | semidirect |
| 152. C17 | C2×#2380 | semidirect |
| 168. C2×D4 | C22×#595 | semidirect |
| 180. C42 | C22×#595 | semidirect |
| 225. C2 | #14545328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545328 | 2 |
| C2×#11763757 | 2 |
| C2×#11763754 | 2 |
| C2×#127×D17 | 2 |
| C2×#2380 | 17 |