Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1566 conjugacy classes of subgroups; only the 424 normal subgroups are shown.
This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 424 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 |
|---|---|---|
| 9. #11763754 | C4 | semidirect |
| 12. C42×#595 | C4 | semidirect |
| 14. #11762677 | C4 | semidirect |
| 15. #11762676 | C4 | semidirect |
| 17. C17×#383 | C4 | semidirect |
| 60. C42×C17 | C42 | semidirect |
| 61. C4×Dic17 | C42 | semidirect |
| 102. #595 | #383 | direct (N × H) |
| 114. #383 | #595 | direct (N × H) |
| 143. C17 | C4×#383 | semidirect |
| 168. C42 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763754 | 2 |
| C2×C42×#595 | 2 |
| #14543959 | 2 |
| #95×#595 | 2 |
| D17×#383 | 2 |
| C4×#383 | 17 |