Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
706 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 172 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 |
|---|---|---|
| 2. #14543608 | C2 | semidirect |
| 6. #11763826 | C4 | semidirect |
| 10. C4×#63247 | C4 | semidirect |
| 41. C4×#3624 | C2×C4 | semidirect |
| 68. C42×C17 | M16 | semidirect |
| 78. C4×Dic17 | M16 | semidirect |
| 180. C17 | #7855 | semidirect |
| 218. C42 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545460 | 2 |
| #14543608 | 2 |
| C2×#11762655 | 2 |
| #7855 | 17 |