Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
524 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 98 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. #14544661 | C2 | semidirect |
| 2. #14544660 | C2 | semidirect |
| 4. #14543647 | C2 | semidirect |
| 20. C2×#10587485 | C4 | semidirect |
| 21. C2×C22⋊#3622 | C4 | semidirect |
| 23. C2×#10587486 | C4 | semidirect |
| 24. C22×M16×C17 | C4 | semidirect |
| 165. C8×C17 | #99 | semidirect |
| 201. C22×M16 | #595 | semidirect |
| 268. C17 | #8610 | semidirect |
| 371. C8 | #10587551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544661 | 2 |
| #14544660 | 2 |
| #14544644 | 2 |
| #14543647 | 2 |
| C2×#11762878 | 2 |
| #8610 | 17 |