Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
920 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 920 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. #14544640 | C2 | semidirect |
| 2. #14544510 | C2 | semidirect |
| 3. C2×#11763653 | C2 | semidirect |
| 50. C22⋊#3624 | D4 | semidirect |
| 256. C17 | #9653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544640 | 2 |
| #14544510 | 2 |
| C2×#11763653 | 2 |
| C2×#11762710 | 2 |
| #9653 | 17 |