Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #14545785 | C2 | semidirect |
| 4. #14545784 | C2 | semidirect |
| 45. C17×C22⋊Q8 | C8 | semidirect |
| 46. #10587632 | C8 | semidirect |
| 47. #10587610 | C8 | semidirect |
| 48. #10587583 | C8 | semidirect |
| 248. C22⋊Q8 | #3633 | semidirect |
| 273. C17 | #7600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545925 | 2 |
| #14545924 | 2 |
| #14545785 | 2 |
| #14545784 | 2 |
| C22⋊Q8×#595 | 2 |
| #7600 | 17 |