Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
662 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 122 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. #14544641 | C2 | semidirect |
| 2. #14544445 | C2 | semidirect |
| 3. #14543602 | C2 | semidirect |
| 4. #14543601 | C2 | semidirect |
| 49. #10587581 | C8 | semidirect |
| 76. C2×D68 | C2×C8 | semidirect |
| 101. C4⋊C4×C17 | C2×C8 | semidirect |
| 275. C17 | #7586 | semidirect |
| 321. C4⋊C4 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544641 | 2 |
| #14544445 | 2 |
| #14543602 | 2 |
| #14543601 | 2 |
| C4×#10587581 | 2 |
| #7586 | 17 |