Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
298 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 75 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. #14531013 | C2 | semidirect |
| 2. #14530834 | C2 | semidirect |
| 4. #14526842 | C2 | semidirect |
| 5. #14526748 | C2 | semidirect |
| 91. D4×C17 | Q32 | semidirect |
| 180. C17 | #12346 | semidirect |
| 220. D4 | #10587500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531013 | 2 |
| #14530834 | 2 |
| #14528149 | 2 |
| #14526842 | 2 |
| #14526748 | 2 |
| D4⋊#63214 | 2 |
| C17×#3338 | 2 |
| #12346 | 17 |