Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
336 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 3. #14543924 | C2 | semidirect |
| 4. #14543923 | C2 | semidirect |
| 5. #14543918 | C2 | semidirect |
| 6. #14543918 | C2 | semidirect |
| 16. #11763422 | C4 | semidirect |
| 18. #11763204 | C4 | semidirect |
| 25. #11762868 | C4 | semidirect |
| 26. C17×#488 | C4 | semidirect |
| 31. C17×#125 | C2×C4 | semidirect |
| 47. #10587555 | C2×C4 | semidirect |
| 56. C4×C8×C17 | C2×C4 | semidirect |
| 61. #10587474 | C2×C4 | semidirect |
| 172. #488 | #595 | semidirect |
| 203. #125 | C2×#595 | semidirect |
| 226. C4×C8 | C2×#595 | semidirect |
| 227. C17 | #13610 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545064 | 2 |
| #14545062 | 2 |
| #14543924 | 2 |
| #14543923 | 2 |
| #14543918 | 2 |
| #14539859 | 2 |
| #13610 | 17 |