Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14531009 | C2 | semidirect |
| 2. D4×#63214 | C2 | semidirect |
| 4. #14526857 | C2 | semidirect |
| 5. #14526842 | C2 | semidirect |
| 6. #14526829 | C2 | semidirect |
| 7. C17×#1675 | C2 | semidirect |
| 95. #1675 | D17 | semidirect |
| 155. C17 | #12468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531009 | 2 |
| D4×#63214 | 2 |
| #14528139 | 2 |
| #14526857 | 2 |
| #14526842 | 2 |
| #14526829 | 2 |
| C17×#1675 | 2 |
| #12468 | 17 |