Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
274 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 89. #3622 | Q32 | semidirect |
| 147. C17 | #12528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531036 | 2 |
| #14531012 | 2 |
| #14531011 | 2 |
| #14528400 | 2 |
| #14528378 | 2 |
| #14526703 | 2 |
| C17×#2247 | 2 |
| #12528 | 17 |