Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
640 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 118 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. #14544570 | C2 | semidirect |
| 2. C4×#10587542 | C2 | semidirect |
| 3. C2×#11763664 | C2 | semidirect |
| 48. #10587542 | D4 | semidirect |
| 153. C4×C17 | #329 | semidirect |
| 214. C17 | #9685 | semidirect |
| 318. C4 | #11763664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544570 | 2 |
| C4×#10587542 | 2 |
| C2×#11763664 | 2 |
| #14537140 | 2 |
| #9685 | 17 |