Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
430 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 96 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. #14545142 | C2 | semidirect |
| 2. #14544341 | C2 | semidirect |
| 3. #14543738 | C2 | semidirect |
| 8. #11763695 | C22 | semidirect |
| 10. #11763672 | C22 | semidirect |
| 63. D8×C17 | M16 | semidirect |
| 176. C17 | #11657 | semidirect |
| 192. D8 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545142 | 2 |
| #14544341 | 2 |
| #14543738 | 2 |
| C2×D8×Dic17 | 2 |
| #11657 | 17 |