Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
516 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 104 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. #14544969 | C2 | semidirect |
| 3. C4×C8×#595 | C2 | semidirect |
| 4. #14544339 | C2 | semidirect |
| 5. #14544133 | C2 | semidirect |
| 20. #11763182 | C4 | semidirect |
| 21. #11763161 | C4 | semidirect |
| 22. #11763157 | C4 | semidirect |
| 26. C17×#498 | C4 | semidirect |
| 86. C4×#595 | SD16 | semidirect |
| 141. C8×C17 | #104 | semidirect |
| 170. #498 | #595 | semidirect |
| 231. C17 | #9843 | semidirect |
| 307. C8 | #10587550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544969 | 2 |
| #14544917 | 2 |
| C4×C8×#595 | 2 |
| #14544339 | 2 |
| #14544133 | 2 |
| #14544131 | 2 |
| #14539345 | 2 |
| #9843 | 17 |