Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
776 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 104 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. #14543779 | C2 | direct (N × H) |
| 15. #11762720 | C4 | semidirect |
| 18. C2×#10587502 | C4 | semidirect |
| 19. C23×Q8×C17 | C4 | semidirect |
| 26. C22×Q8×C17 | C2×C4 | semidirect |
| 50. #10587502 | C2×C4 | semidirect |
| 201. C23×Q8 | #595 | semidirect |
| 219. C2×C17 | #1351 | semidirect |
| 231. C22×Q8 | C2×#595 | semidirect |
| 257. C17 | C2×#1351 | semidirect |
| 409. C2 | #14543779 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763687 | 2 |
| C2×#11763653 | 2 |
| #14543779 | 2 |
| C2×#11762720 | 2 |
| C2×#1351 | 17 |