Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
628 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×Q8⋊#3633 | C2 | semidirect |
| 4. #14545792 | C2 | semidirect |
| 53. C17×C22⋊Q8 | C8 | semidirect |
| 54. #10587632 | C8 | semidirect |
| 55. #10587610 | C8 | semidirect |
| 56. #10587583 | C8 | semidirect |
| 260. C22⋊Q8 | #3633 | semidirect |
| 291. C17 | #8938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763922 | 2 |
| C4×C22⋊#3633 | 2 |
| C2×Q8⋊#3633 | 2 |
| #14545792 | 2 |
| C22⋊Q8×#595 | 2 |
| #8938 | 17 |