Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
344 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 54 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. #14545084 | C2 | semidirect |
| 2. #14545060 | C2 | semidirect |
| 3. #14543932 | C2 | semidirect |
| 4. #14543931 | C2 | semidirect |
| 5. #14543911 | C2 | semidirect |
| 6. #14543911 | C2 | semidirect |
| 16. #11763413 | C4 | semidirect |
| 19. #11763173 | C4 | semidirect |
| 25. #11762868 | C4 | semidirect |
| 26. C17×#493 | C4 | semidirect |
| 34. C17×#127 | C2×C4 | semidirect |
| 47. #10587556 | C2×C4 | semidirect |
| 54. C4×C8×C17 | C2×C4 | semidirect |
| 61. #10587474 | C2×C4 | semidirect |
| 173. #493 | #595 | semidirect |
| 205. #127 | C2×#595 | semidirect |
| 230. C4×C8 | C2×#595 | semidirect |
| 231. C17 | #13605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545084 | 2 |
| #14545060 | 2 |
| #14543932 | 2 |
| #14543931 | 2 |
| #14543911 | 2 |
| #14539827 | 2 |
| #13605 | 17 |