Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
726 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 192 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. #14545509 | C2 | semidirect |
| 2. #14544384 | C2 | semidirect |
| 3. #14544343 | C2 | semidirect |
| 4. #14544131 | C2 | semidirect |
| 5. #14543980 | C2 | semidirect |
| 77. #63242 | D8 | semidirect |
| 193. C17 | #17975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545509 | 2 |
| #14544384 | 2 |
| #14544343 | 2 |
| #14544131 | 2 |
| #14543980 | 2 |
| #14539364 | 2 |
| #17975 | 17 |