Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
700 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 106 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. #14544511 | C2 | semidirect |
| 2. C2×#11763663 | C2 | semidirect |
| 4. #14543962 | C2 | semidirect |
| 14. C2×#10587633 | C4 | semidirect |
| 18. #11762711 | C4 | semidirect |
| 23. #11762674 | C4 | semidirect |
| 24. C17×#391 | C4 | semidirect |
| 243. #391 | #595 | semidirect |
| 307. C17 | #9682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544511 | 2 |
| C2×#11763663 | 2 |
| C2×#11763661 | 2 |
| #14543962 | 2 |
| #14537088 | 2 |
| #9682 | 17 |